Correction of birefringence in cubic crystalline optical systems

ABSTRACT

An optical system includes multiple cubic crystalline optical elements aligned along a common optical axis and having their crystal lattices oriented with respect to each other to minimize the effects of intrinsic birefringence and produce a system with reduced retardance. The optical system may be a refractive or catadioptric system having a high numerical aperture and using light with a wavelength at or below 248 nanometers. The net retardance of the system is less than the sum of the retardance contributions of the respective optical elements as the elements are oriented such that the intrinsic birefringences of the individual elements cancel each other out. In one embodiment, two [110] cubic crystalline optical elements are clocked with respect to one another and used in conjunction with a [100] cubic crystalline optical element to reduce retardance. Various birefringent elements, wave plates, and combinations thereof provide additional correction for residual retardance and wavefront aberrations. The optical system may be used in a photolithography tool to pattern substrates such as semiconductor substrates and thereby produce semiconductor devices.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/071,375, entitled CORRECTION OF BIREFRINGENCE IN CUBIC CRYSTALLINEOPTICAL SYSTEMS. filed Feb. 7, 2002, now U.S. Pat. No. 6,683,710 whichclaims priority of U.S. Provisional Application Ser. No. 60/295,212,entitled MEANS TO DETERMINE, CORRECT AND ADJUST FOR INTRINSICBIREFRINGENCE IN OPTICAL MATERIALS FOR USE IN LITHOGRAPHY LENSES, filedJun. 1, 2001; U.S. Provisional Application Ser. No. 60/296,694, entitledMEANS TO DETERMINE, CORRECT AND ADJUST FOR INTRINSIC BIREFRINGENCE INOPTICAL MATERIALS FOR USE IN LITHOGRAPHY LENSES, filed Jun. 6, 2001;U.S. Provisional Application Ser. No. 60/299,497, entitled CORRECTION OFINTRINSIC BIREFRINGENCE IN OPTICAL SYSTEMS USING CUBIC CRYSTALMATERIALS, filed Jun. 20, 2001; U.S. Provisional Application Ser. No.60/299,603, entitled CORRECTION OF INDUCED BIREFRINGENCE IN CUBICCRYSTALS, filed Jun. 20, 2001; U.S. Provisional Application Ser. No.60/335,093, entitled INTRINSIC BIREFRINGENCE COMPENSATION, filed Oct.30, 2001; and U.S. Provisional Application Ser. No. 60/332,183, entitledCOMPENSATION FOR INTRINSIC BIREFRINGENCE EFFECTS IN CUBIC CRYSTALLINEOPTICAL SYSTEMS, filed Nov. 21, 2001.

FIELD OF THE INVENTION

The present invention relates, most generally, to high performanceoptical systems and lithography methods. More particularly, the presentinvention relates to an apparatus and method for compensating for theeffects of intrinsic birefringence in optical systems using cubiccrystalline optical elements.

BACKGROUND OF THE INVENTION

In order to increase levels of device integration for integrated circuitand other semiconductor devices, there is a drive to produce devicefeatures having smaller and smaller dimensions. In today's rapidlyadvancing semiconductor manufacturing industry, there is a related driveto produce such device features in a reliable and repeatable manner.

Optical lithography systems are commonly used in the fabrication processto form images of device patterns upon semiconductor substrates. Theresolving power of such systems is proportional to the exposurewavelength; therefore, it is advantageous to use exposure wavelengthsthat are as short as possible. For sub-micron lithography, deepultraviolet light having a wavelength of 248 nanometers or shorter iscommonly used. Wavelengths of interest include 193 and 157 nanometers.

At ultraviolet or deep ultraviolet wavelengths, the materials used toform the lenses, windows, and other optical elements of the lithographysystem, are of critical significance. Such optical elements must becompatible with the short wavelength light used in these lithographysystems.

Calcium fluoride and other cubic crystalline materials such as bariumfluoride, lithium fluoride, and strontium fluoride, represent some ofthe materials being developed for use as optical elements for 157nanometer lithography, for example. These single crystal fluoridematerials have a desirably high transmittance compared to ordinaryoptical glass and can be produced with good homogeneity.

Accordingly, such cubic crystalline materials are useful as opticalelements in short wavelength optical systems such as wafer steppers andother projection printers used to produce small features on substratessuch as semiconductor and other wafers used in the semiconductormanufacturing industry. In particular, calcium fluoride finds particularadvantage in that it is an easily obtained cubic crystalline materialand large high purity single crystals can be grown.

A primary concern for the use of cubic crystalline materials for opticalelements in deep ultraviolet lithography systems is anisotropy ofrefractive index inherent in cubic crystalline materials; this isreferred to as “intrinsic birefringence.” It has been recently reported[J. Burnett, Z. H. Levine, and E. Shipley, “Intrinsic Birefringence in157 nm materials,” Proc. 2nd Intl. Symp on 157 nm Lithography, Austin,Intl SEMATEC, ed. R. Harbison, 2001] that cubic crystalline materialssuch as calcium fluoride, exhibit intrinsic birefringence that scales asthe inverse of the square of the wavelength of light used in the opticalsystem. The magnitude of this birefringence becomes especiallysignificant when the optical wavelength is decreased below 250nanometers and particularly as it approaches 100 nanometers. Ofparticular interest is the effect of intrinsic birefringence at thewavelength of 157 nanometers (nm), the wavelength of light produced byan F₂ excimer laser favored in the semiconductor manufacturing industry.

Birefringence, or double-refraction, is a property of refractivematerials in which the index of refraction is anisotropic. For lightpropagating through a birefringent material, the refractive index variesas a function of polarization and orientation of the material withrespect to the propagation direction. Unpolarized light propagatingthrough a birefringent material will generally separate into two beamswith orthogonal polarization states.

When light passes through a unit length of a birefringent material, thedifference in refractive index for the two ray paths will result in anoptical path difference or retardance. Birefringence is a unitlessquantity, although it is common practice in the lithography community toexpress it in units of nm/cm. Birefringence is a material property,while retardance is an optical delay between polarization states. Theretardance for a given ray through an optical system may be expressed innm, or it may be expressed in terms of number of waves of a particularwavelength.

In uniaxial crystals, such as magnesium fluoride or crystal quartz, thedirection through the birefringent material in which the two refractedbeams travel with the same velocity is referred to as the birefringenceaxis. The term optic axis is commonly used interchangeably withbirefringence axis when dealing with single crystals. In systems of lenselements, the term optical axis usually refers to the symmetry axis ofthe lens system. To avoid confusion, the term optical axis will be usedhereinafter only to refer to the symmetry axis in a lens system. Fordirections through the material other than the birefringence axis, thetwo refracted beams will travel with different velocities. For a givenincident ray upon a birefringent medium, the two refracted rays arecommonly described as the ordinary and extraordinary rays. The ordinaryray is polarized perpendicular to the birefringence axis and refractsaccording to Snell's Law, and the extraordinary ray is polarizedperpendicular to the ordinary ray and refracts at an angle that dependson the direction of the birefringence axis relative to the incident rayand the amount of birefringence. In uniaxial crystals, the birefringenceaxis is oriented along a single direction, and the magnitude of thebirefringence is constant throughout the material. Uniaxial crystals arecommonly used for optical components such as retardation plates andpolarizers.

In contrast, however, cubic crystals have been shown to have both abirefringence axis orientation and magnitude that vary depending on thepropagation direction of the light with respect to the orientation ofthe crystal lattice. In addition to birefringence, which is thedifference in the index of refraction seen by the twoeigenpolarizations, the average index of refraction also varies as afunction of angle of incidence, which produces polarization independentphase errors.

Crystal axis directions and planes are described herein using Millerindices, which are integers with no common factors and that areinversely proportional to the intercepts of the crystal planes along thecrystal axes. Lattice planes are given by the Miller indices inparentheses, e.g. (100), and axis directions in the direct lattice aregiven in square brackets, e.g. [111]. The crystal lattice direction,e.g. [111], may also be referred to as the [111] crystal axis of thematerial or optical element. The (100), (010), and (001) planes areequivalent in a cubic crystal and are collectively referred to as the{100} planes. For example, light propagating through an exemplary cubiccrystalline optical element along the [110] crystal axis experiences themaximum birefringence, while light propagating along the [100] crystalaxis experiences no birefringence.

Thus, as a wavefront propagates through an optical element constructedfrom a cubic crystalline material, the wavefront may be retarded becauseof the intrinsic birefringence of the optical element. The retardancemagnitude and orientation may each vary, because the local propagationangle through the material varies across the wavefront. Such variationsmay be referred to as “retardance aberrations.” Retardance aberrationssplit a uniformly polarized wavefront into two wavefronts withorthogonal polarizations. Each of the orthogonal wavefronts willexperience a different refractive index, resulting in differentwavefront aberrations. These aberrations are capable of significantlydegrading image resolution and introducing distortion of the image fieldat the wavelengths of interest, such as 157 nm, particularly forsub-micron projection lithography in semiconductor manufacturing. It canbe therefore seen that there is a need in the art to compensate forwavefront aberrations caused by intrinsic birefringence of cubiccrystalline optical elements, which can cause degradation of imageresolution and image field distortion, particularly in projectionlithography systems using light having wavelengths in the deepultraviolet range.

SUMMARY OF THE INVENTION

To address these and other needs, and in view of its purposes, thepresent invention provides a method and apparatus for preventingintrinsic birefringence in cubic crystalline optical systems fromcausing wavefront aberrations. The crystal axes of the cubic crystallinelens elements are oriented to minimize net retardance by balancing theretardance contributions from the individual lens elements.

In one exemplary embodiment, the present invention provides an opticalsystem which includes a projection lens formed of a plurality of opticalelements, two or more of which are constructed from cubic crystallinematerial and oriented with their [110] cubic crystalline latticedirection along the system optical axis and with relative rotationsabout the optical axis to give reduced retardance for light propagatingat small angles relative to the system optical axis, and one or moreelements oriented with the optical axis substantially along the [100]cubic crystalline lattice direction to give reduced retardance foroff-axis light propagating at larger angles with respect to the systemoptical axis.

In another exemplary embodiment, the present invention provides anoptical system which includes four optical elements which areconstructed from cubic crystalline material and oriented with theoptical axis substantially along their [110] cubic crystalline latticedirections. The optical elements are oriented about the optical axis togive reduced retardance for light propagating at small angles relativeto the system optical axis. The system further includes an opticalelement oriented with its [100] crystal lattice direction substantiallyalong the optical axis to give reduced retardance for light propagatingat larger angles with respect to the system optical axis.

In another exemplary embodiment, the present invention provides anoptical system that includes a plurality of optical elements, two ormore of which are constructed from cubic crystalline material andoriented with their [110] cubic crystalline lattice direction along theoptical axis of the system, and with relative rotations about theoptical axis to give reduced retardance for light propagating at smallangles relative to the [110] lattice direction. A stress-inducedbirefringence is applied to either a [110] cubic crystal optical elementor a further optical element such as a non-cubic crystalline element ora [100] optical element, to reduce residual retardance of the opticalsystem.

In another exemplary embodiment, the present invention provides a methodand apparatus for reducing retardance aberrations caused by intrinsicbirefringence by providing a lens system, orienting two or more elementswith the optical axis substantially along the [110] cubic crystallinelattice directions of the elements and one or more elements with theoptical axis substantially along the [100] cubic crystalline latticedirections of the elements, and providing optimized relative rotationsof the elements about the optical axis.

In another exemplary embodiment, the present invention provides a methodand apparatus for reducing retardance aberrations caused by intrinsicbirefringence by providing a lens system defined by a lens prescription,then splitting at least one of the elements of the lens system intomultiple cubic crystalline components, oriented to reduce retardanceaberrations while maintaining the overall element dimensions defined bythe lens prescription.

In yet another exemplary embodiment, the present invention provides amethod and apparatus for reducing retardance caused by intrinsicbirefringence by providing a lens system with at least two cubiccrystalline optical elements and providing a stress-inducedbirefringence to at least one of the optical elements to reduce residualretardance variations.

Another aspect of the present invention is an apparatus and method forcompensating for residual astigmatism due to variations in the averageindex of refraction in the cubic crystalline optical elements, throughthe use of at least one optical element whose base radius of curvaturediffers in orthogonal directions.

In another exemplary embodiment, the present invention provides aphotolithography tool including one of the above-described opticalsystems.

In another exemplary embodiment, the present invention provides a methodand apparatus for using the selectively oriented crystalline lenselements to form semiconductor devices on semiconductor substrates usedin the semiconductor manufacturing industry.

In another exemplary embodiment, the present invention provides asemiconductor device formed using a lithography tool including theselectively oriented cubic crystalline lens elements.

BRIEF DESCRIPTION OF THE DRAWING

The present invention is best understood from the following detaileddescription when read in conjunction with the accompanying drawing. Itis emphasized that, according to common practice, the various featuresof the drawing are not to scale. On the contrary, the dimensions of thevarious features are arbitrarily expanded or reduced for clarity.Included in the drawing are the following figures:

FIG. 1 is a schematic illustration of the projection optics of anexemplary lithography system;

FIG. 2 is a schematic illustration of an exemplary lithography system;

FIG. 3A is a graphical representation of variation of birefringence axisorientation with respect to a cubic crystal lattice;

FIG. 3B is a graphical representation of variation of birefringencemagnitude with respect to a cubic crystal lattice;

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice;

FIG. 5A is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [110] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5B is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [100] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 5C is a graphical illustration of birefringence magnitude andbirefringence axis orientation in angular space for a cubic crystallinematerial with respect to the [111] lattice direction and indicates theazimuthal orientations of the off-axis peak birefringence lobes;

FIG. 6 is a schematic illustration of an exemplary optical system withthree cubic crystalline elements concentric about the focal point of aconverging beam;

FIG. 7A is a graphical illustration of net retardance magnitude andorientation across the pupil for an exemplary embodiment of the opticalsystem depicted in FIG. 6 in which the optical axis extends along the[110] lattice direction for each element and the crystal axes for allelements are oriented identically;

FIG. 7B is a graphical illustration of net retardance magnitude andorientation across the pupil for an exemplary embodiment of the opticalsystem depicted in FIG. 6 in which the optical axis extends along the[100] lattice direction for each element and the crystal axes for allelements are oriented identically;

FIG. 7C is a graphical illustration of net retardance magnitude andorientation across the pupil for an exemplary embodiment of the opticalsystem depicted in FIG. 6 in which the optical axis extends along the[111] lattice direction for each element and the crystal axes for allelements are oriented identically;

FIG. 8A is a graphical illustration showing the individual contributionto the retardance across the pupil for the first element of the opticalsystem depicted in FIG. 6, in which the first element is a [110] opticalelement and is rotated about the optical axis such that horizontallyoriented retardance is produced along the optical axis;

FIG. 8B is a graphical illustration showing the individual contributionto the retardance across the pupil for the second element of the opticalsystem depicted in FIG. 6, in which the second element is a [110]optical element and is rotated about the optical axis such thatvertically oriented retardance is produced along the optical axis;

FIG. 8C is a graphical illustration showing the individual contributionto the retardance across the pupil for the third element of the opticalsystem depicted in FIG. 6, in which the third element is a [100] opticalelement and is rotated about the optical axis such that the peakretardance is oriented along the pupil diagonals;

FIG. 9A is a graphical illustration showing the combined retardanceacross the pupil for the first and second elements of the optical systemdepicted in FIG. 6 according to the exemplary embodiment in which thefirst two elements are [110] cubic crystalline optical elements and thethird element is a [100] cubic crystalline optical element;

FIG. 9B is a graphical illustration showing the net retardance acrossthe pupil for the optical system depicted in FIG. 6 according to theexemplary embodiment in which the first two elements are [110] cubiccrystalline optical elements and the third element is a [100] cubiccrystalline optical element;

FIG. 9C is a graphical illustration showing the net retardance acrossthe pupil for an optical system depicted in FIG. 6 according to anotherexemplary embodiment in which the first two elements are [110] cubiccrystalline optical elements and the third element is a [100] cubiccrystalline optical element and in which the third element includes athickness selected to minimize the net RMS retardance;

FIG. 9D is a graphical illustration plotting the radial retardancevariation across the first element in the optical system depicted inFIG. 6, when a compressive hoop stress is applied around the perimeterof the first element;

FIG. 9E is a graphical illustration showing the individual contributionto the retardance across the pupil for the first element of the opticalsystem depicted in FIG. 6, when an exemplary tensile hoop stress isapplied around the perimeter of the element, and without including theretardance caused by intrinsic birefringence;

FIG. 9F is a graphical illustration showing the net retardance acrossthe pupil for the optical system depicted in FIG. 6, when an exemplarytensile hoop stress is applied around the perimeter of the first elementto minimize the net RMS retardance;

FIG. 10 is a schematic illustration showing an exemplary optical systemwith five cubic crystalline elements concentric about the focal point ofa converging beam;

FIG. 11A is a graphical illustration showing net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 10 in which the optical axis is alongthe [110] lattice direction for each element and the crystal axes forall elements are oriented identically;

FIG. 11B is a graphical illustration showing net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 10 in which the optical axis is alongthe [100] lattice direction for each element and the crystal axes forall elements are oriented identically;

FIG. 11C is a graphical illustration showing net retardance magnitudeand orientation across the pupil for an exemplary embodiment of theoptical system depicted in FIG. 10 in which the optical axis is alongthe [111] lattice direction for each element and the crystal axes forall elements are oriented identically;

FIGS. 12A-14C are each graphical illustrations showing retardancemagnitude and orientation for the optical system shown in FIG. 10, inwhich the first four elements are [110] cubic crystalline opticalelements and the fifth element is a [100] cubic crystalline opticalelement: FIG. 12A shows the individual contribution to the retardanceacross the pupil for the first element, in which the retardance alongthe optical axis is rotated by 17.632° with respect to horizontal;

FIG. 12B shows the individual contribution to the retardance across thepupil for the second element, in which the retardance along the opticalaxis is rotated by −17.632° with respect to horizontal;

FIG. 12C shows the individual contribution to the retardance across thepupil for the third element, in which the retardance along the opticalaxis is rotated by 72.368° with respect to horizontal;

FIG. 12D shows the individual contribution to the retardance across thepupil for the fourth element, in which the retardance along the opticalaxis is rotated by −72.368° with respect to horizontal;

FIG. 13A shows the retardance across the pupil for the first and thirdelements overlapping one another;

FIG. 13B shows the net retardance across the pupil for the first andthird elements;

FIG. 13C shows the net retardance across the pupil for the second andfourth elements;

FIG. 14A shows the net retardance across the pupil for the first fourelements;

FIG. 14B shows the individual contribution to the retardance across thepupil for the fifth element;

FIG. 14C shows the net retardance across the pupil;

FIG. 15 is a schematic illustration of an exemplary large format,refractive projection lens;

FIGS. 16A and 16B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 15 at central andextreme field points, respectively, due to single-layer anti-reflectioncoatings;

FIGS. 17A and 17B are graphical illustrations showing diattenuationacross the pupil for the exemplary lens depicted in FIG. 15 at centraland extreme field points, respectively, due to single-layeranti-reflection coatings;

FIGS. 18A, 18B, 18C, and 18D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 15: FIG. 18Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 18B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 18C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 18Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

FIGS. 19A and 19B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 15 at central andextreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [110] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

FIGS. 20A and 20B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 15 at central andextreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [100] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

FIGS. 21A and 21B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 15 at central andextreme field points, respectively, in which all elements are cubiccrystals identically aligned in three dimensions, with the optical axisextending along the [111] crystal lattice direction and a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

FIG. 22 is a schematic illustration showing the exemplary lens depictedin FIG. 15, with the crystal axes of the elements selected and orientedto compensate for intrinsic birefringence, in which the hatched elementsare [100] cubic crystalline optical elements and all others are [110]cubic crystal optical elements;

FIGS. 23A and 23B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 22 at central andextreme field points, respectively, due to anti-reflection coatings andintrinsic birefringence of all elements;

FIGS. 24A, 24B, 24C, and 24D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 22. FIG. 24Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 24B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 24C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 24Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

FIGS. 25A and 25B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens shown in FIG. 1 at central and extremefield points, respectively due to single-layer anti-reflection coatings;

FIGS. 26A and 26B are graphical illustrations showing diattenuationacross the pupil for the exemplary lens depicted in FIG. 1 at centraland extreme field points, respectively due to single-layeranti-reflection coatings;

FIGS. 27A, 27B, 27C, and 27D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 1. FIG. 27Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 27B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 27C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 27Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

FIGS. 28A and 28B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 1 at central andextreme field points, respectively, in which all elements areidentically aligned in three dimensions, with their [110] crystallattice direction along the optical axis and including a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

FIGS. 29A and 29B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 1 at central andextreme field points, respectively, in which all elements areidentically aligned in three dimensions, with their [100] crystallattice direction along the optical axis and including a peakbirefringence magnitude corresponding to that of calcium fluoride at awavelength of 157 nm;

FIGS. 30A and 30B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 1 at central and extreme fieldpoints, respectively, in which all elements are identically aligned inthree dimensions, with their [111] crystal lattice direction along theoptical axis and including a peak birefringence magnitude correspondingto that of calcium fluoride at a wavelength of 157 nm;

FIG. 31 is a schematic illustration showing the exemplary lens depictedin FIG. 1 with the last two elements split into two segments withdifferent relative rotations about the optical axis and the crystal axesof the elements oriented to compensate for intrinsic birefringence, inwhich the hatched elements have their [100] crystal lattice directionalong the optical axis and all others are oriented along with their[110] crystal lattice direction along the optical axis;

FIGS. 32A and 32B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 31 at central andextreme field points, respectively, due to anti-reflection coatings andintrinsic birefringence of all elements;

FIGS. 33A, 33B, 33C, and 33D are contour plots showing the residualwavefront error for the exemplary lens depicted in FIG. 31. FIG. 33Ashows the wavefront error for an input polarization in the X directionused with an exit pupil analyzer in the X direction for the centralfield point. FIG. 33B shows the wavefront error for an inputpolarization in the X direction used with an exit pupil analyzer in theX direction for the extreme field point. FIG. 33C shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the central field point. FIG. 33Dshows the wavefront error for an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the extremefield point;

FIG. 34 is a schematic illustration showing an exemplary large format,catadioptric projection lens;

FIGS. 35A and 35B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 34 at central and extreme fieldpoints, respectively due to single-layer anti-reflection coatings;

FIGS. 36A, 36B, 36C, and 36D are contour plots showing the residualwavefront error for the lens depicted in FIG. 34. FIG. 36A shows thewavefront error for an input polarization in the X direction used withan exit pupil analyzer in the X direction for the central field point.FIG. 36B shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for theextreme field point. FIG. 36C shows the wavefront error for an inputpolarization in the Y direction used with an exit pupil analyzer in theY direction for the central field point. FIG. 36D shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the extreme field point;

FIGS. 37A and 37B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 34 at central and extreme fieldpoints, respectively, in an exemplary embodiment in which all elementsbetween the second wave plate and the image plane are identicallyaligned in three dimensions, with the optical axis along the [110]crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 38A and 38B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 34 at central and extreme fieldpoints, respectively, in an exemplary embodiment in which all elementsbetween the second wave plate and the image plane are identicallyaligned in three dimensions, with the optical axis along the [100]crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIGS. 39A and 39B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 34 at central and extreme fieldpoints, respectively, in an exemplary embodiment in which all elementsbetween the second wave plate and the image plane are identicallyaligned in three dimensions, with the optical axis along the [111]crystal lattice direction and a peak birefringence magnitudecorresponding to that of calcium fluoride at a wavelength of 157 nm;

FIG. 40 is a schematic illustration of the exemplary lens shown in FIG.34 with the last element of FIG. 34 split into two sub-elements, inwhich the hatched elements are [110] cubic crystalline optical elements,and all others are [100] cubic crystalline optical elements;

FIGS. 41A and 41B are graphical illustrations showing retardance acrossthe pupil for the exemplary lens depicted in FIG. 40 at central andextreme field points, respectively, due to anti-reflection coatings andthe intrinsic birefringence of the front six elements, with the crystallattice orientation of the front six elements chosen to minimize thevariation in the retardance along horizontal and vertical directions;

FIGS. 42A and 42B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 40 at central and extreme fieldpoints, respectively, due to anti-reflection coatings and intrinsicbirefringence of the group of elements between the second wave plate andthe image plane;

FIGS. 43A and 43B are graphical illustrations showing retardance acrossthe pupil for the lens depicted in FIG. 40 at central and extreme fieldpoints, respectively, due to anti-reflection coatings and intrinsicbirefringence of all elements;

FIGS. 44A, 44B, 44C, and 44D are contour plots showing the residualwavefront error for the lens depicted in FIG. 40. FIG. 44A shows thewavefront error for an input polarization in the X direction used withan exit pupil analyzer in the X direction for the central field point.FIG. 44B shows the wavefront error for an input polarization in the Xdirection used with an exit pupil analyzer in the X direction for theextreme field point. FIG. 44C shows the wavefront error for an inputpolarization in the Y direction used with an exit pupil analyzer in theY direction for the central field point. FIG. 44D shows the wavefronterror for an input polarization in the Y direction used with an exitpupil analyzer in the Y direction for the extreme field point;

FIG. 45 is a schematic illustration of an exemplary optical system withtwo cubic crystalline elements concentric about the focal point of aconverging beam;

FIG. 46A is a graphical illustration showing the individual contributionto the retardance across the pupil for the first element of the opticalsystem depicted in FIG. 45, when an exemplary compressive hoop stress isapplied around the perimeter of the element, without including theretardance caused by intrinsic birefringence; and

FIG. 46B is a graphical illustration showing the net retardance acrossthe pupil for the optical system depicted in FIG. 45, when an exemplarycompressive hoop stress is applied around the perimeter of the elementto minimize the net RMS retardance.

DETAILED DESCRIPTION OF THE INVENTION

It is known in the art that cubic crystalline materials favored in highperformance lithography systems, such as the photolithographic toolsused in the semiconductor manufacturing industry, exhibit intrinsicbirefringence, i.e., an inherent anisotropy in refractive index. Whenused for construction of elements of an optical system, the birefringentproperties of these cubic crystalline materials may produce wavefrontaberrations that significantly degrade image resolution and introducefield distortion. This is especially true for the demanding resolutionand overlay requirements in today's semiconductor manufacturingindustry, which emphasizes increased levels of integration and reducedfeature sizes.

The present invention utilizes the concept that both the birefringencedirection and magnitude can be determined for a cubic crystallinematerial and that optical elements may be formed and aligned to balance,or compensate for, the retardance aberrations caused by the intrinsicbirefringence contributions of the individual elements. For example, theintrinsic birefringence variation within the three-dimensional latticeorientation can be determined for these materials. Furthermore, when aplurality of cubic crystalline optical elements is aligned such thateach of the optical elements has a specified three-dimensional latticeorientation with respect to a common optical axis, the plurality ofaligned optical elements will have a net retardance that varies in aknown manner.

This invention relates to a technique to compensate for the effects ofintrinsic birefringence in optical systems employing cubic crystallineoptical elements. The compensation is achieved through proper selectionof the crystal axis directions of the individual optical elements and isapplicable to optical systems using polarized or unpolarized radiation.In one exemplary embodiment, the compensation may be achieved byutilizing a sufficient number of cubic crystalline optical elements withthe optical axis along their [110] crystal lattice direction. Theinvention also provides for compensating for residual astigmatism due tovariations in the average index of refraction in various exemplary cubiccrystalline optical systems. In one exemplary embodiment, thiscompensation may be achieved by varying the base radius of curvature ofat least one optical element, in orthogonal directions.

The various exemplary cubic crystalline optical systems and methods forforming aberration-free patterns on semiconductor substrates areparticularly advantageous as feature sizes become increasingly smallerand approach the half wavelength of the light used to produce thepatterns. Such techniques find particular advantage in high numericalaperture (NA) lens systems but the various aspects of the presentinvention find application in optical systems having both relativelyhigh and relatively low numerical apertures.

FIG. 1 is a schematic illustration showing an exemplary projectionoptics section of an exemplary lithography system. The optical systemshown in FIG. 1 is substantially similar to the optical system shown anddescribed in the seventh embodiment of European Patent EP 1 139 138 A1,issued to K. Omura on Apr. 10, 2001, the contents of which are hereinincorporated by reference. The exemplary optical system may be a largeformat refractive projection lens operating at an NA of 0.75, a peakwavelength of 193.3 nm and 4× reduction. Such an optical system isintended to be exemplary only and other optical systems may be used inother exemplary embodiments. Exemplary optical system 2 may be theprojection optics section of a lithography tool 4 in an exemplaryembodiment. In the exemplary embodiment, optical system 2 is aprojection lens disposed between exemplary reticle 6 and substrate 12.Reticle 6 may be considered to include the object field with the imagefield formed on substrate 12.

Optical system 2 is a lens system, commonly referred to collectively asa “lens,” composed of a plurality of individual lens elements L, opticalaxis 10, and aperture stop (AS) 9. Reticle 6 includes a mask patternwhich is to be projected onto surface 13 of substrate 12. According toan exemplary embodiment, substrate 12 may be a semiconductor wafer usedin the semiconductor manufacturing industry, and surface 13 may becoated with a photosensitive material, such as a photoresist commonlyused in the semiconductor manufacturing industry. Other substrates maybe used according to other exemplary embodiments. According to otherexemplary embodiments within various microlithography tools, reticle 6may be a photomask. Generally speaking, the reticle or photomask,hereinafter referred to collectively as reticle 6, is a medium whichincludes a pattern of clear and opaque sections that form the objectfield. Light is projected through the pattern and the pattern isprojected through the lens system and onto surface 13 of substrate 12.The pattern projected from the reticle 6 onto substrate surface 13 maybe uniformly reduced in size to various degrees such as 10:1, 5:1, 4:1or others, according to the various exemplary embodiments. The exemplarysystem may include a numerical aperture, NA, of 0.75, but systems havingother numerical apertures, such as within the range of 0.60 to 0.90, maybe used alternatively.

The arrangement of the plurality of lens elements L, is intended to beexemplary only and various other arrangements of individual lenselements having various shapes may be used according to other exemplaryembodiments. The element thicknesses, spacings, radii of curvature,aspheric coefficients, and the like, are considered to be the lensprescription. The lens system or “lens” of the present invention ispreferably formed of a plurality of individual lens elements L, one ormore of which may be constructed with cubic crystalline material. Cubiccrystalline materials such as strontium fluoride, barium fluoride,lithium fluoride, and calcium fluoride may be used. Calcium fluoride isthe preferred material. In an exemplary embodiment, each of the cubiccrystalline optical elements will be formed of the same cubiccrystalline material. The lens may include lens elements L which areformed of non-cubic crystalline material such as low-OH fused silica,also known as dry fused silica. Each of the individual lens elements, L,is arranged along a common optical axis 10. In the exemplary embodiment,optical axis 10 is linear.

FIG. 2 is a schematic illustration showing optical system 2 functioningas the projection optics section within lithography tool 4. FIG. 2 showsoptical source 8 and substrate 12. Reticle 6 is disposed betweencondenser optics 14 and projection optics 2 and includes the pattern tobe projected onto substrate 12. The optical field of reticle 6 may be ofvarious dimensions. Each of projection optics 2 and condenser optics 14may include an aperture stop and a plurality of lens elements, windows,and other refractive and reflective members. The optical system shown inFIG. 2 includes linear optical axis 10 and lithography tool 4 may be awafer stepper, projection printer, or other photolithography ormicrolithography tool used in the semiconductor industry. Lithographytool 4 may likewise be a scanning optical system, a step-and-repeatoptical system or other microlithography or projection optics system. Ina scanning-type optical system, a pattern on reticle 6 is projected andscanned onto corresponding sections of surface 13 of substrate 12. In astep-and-repeat optical system, such as a conventional wafer stepper,the pattern on reticle 6, is projected onto multiple different portionsof surface 13 in a plurality of discrete operations. Reticle 6 isconsidered to be at the object field of lithography tool 4, whilesubstrate 12 is considered to be at the image field of lithography tool4. The reticle pattern includes various field points which are projectedonto surface 13 simultaneously.

In an exemplary embodiment, the pattern printed on reticle 6 will beused to create a circuit pattern on surface 13 for an integrated circuitdevice being formed on substrate 12. According to an exemplaryembodiment, the pattern may be projected onto a photosensitive materialformed on surface 13 to form an exposure pattern. The exposure patternmay be developed using conventional means, to produce a photo pattern inthe photosensitive material. The photo pattern may be translated intothe substrate by etching or other means. According to other exemplaryembodiments, substrate 12 may include a series of layers of materialsformed thereon. In this embodiment, surface 13 may be one of the layersand the photo pattern formed on the layer. Etching or other means may beused to translate the photo pattern into the layer. Similary-formedphoto patterns may be used to enable spatially selective doping usingknown methods such as ion implantation. In this manner, multiplephotolithographic operations using the techniques of the presentinvention, may be used to form various circuit patterns in variouslayers to create a completed semiconductor device such as an integratedcircuit. An advantage of the present invention is that images formed onthe substrate have sufficiently low aberration to enable preciselydimensioned and aligned device features to be formed having reducedsizes.

In an exemplary scanning optical system, the optical field of reticle 6which is projected and scanned onto the substrate surface may have aheight of 26 millimeters and a width of a few millimeters. Other fielddimensions may be used according to other exemplary embodiments anddepending on the type of lithography tool in which the projection opticsare included.

Optical source 8 produces a light that is subsequently shaped andconditioned by condenser lens 14. The optical wavelength of source 8 mayvary, and may be no greater than 248 nanometers in an exemplaryembodiment. In one exemplary embodiment, light having a wavelength ofabout 157 nanometers may be used. In an exemplary embodiment, opticalsource 8 may produce linearly polarized light. One optical source whichproduces linearly polarized light is an excimer laser. According toother exemplary embodiments, optical source 8 may produce light which isnon-polarized. According to various exemplary embodiments, a KrF excimerlaser operating at about 248 nm, an ArF excimer laser operating at about193 nm, or an F₂ excimer laser operating at about 157 nm, may be used asoptical source 8.

The light produced by the optical source, shaped and conditioned by thecondenser lens and used to project an image from the reticle orphotomask onto the substrate, may be described as a light beam comprisedof a plurality of rays. Light rays emanating from an individual objectfield point on the reticle or photomask form a wavefront that isprojected by the projection lens to a corresponding image field point atthe substrate. The chief ray is the ray from a given field point thatpasses through the center of the aperture stop and system pupils. For anobject field point located where the optical axis intersects thereticle, the chief ray travels along the optical axis. The full imagefield is therefore generated by a plurality of wavefronts.

Although described in conjunction with a lithography tool used topattern substrates in the semiconductor industry, the various exemplaryoptical systems of the present invention are useful in any applicationin which a pattern is projected through an optical system, onto asubstrate.

FIG. 3A is a three dimensional vector plot showing the spatial variationin birefringence axis orientation within a material having a cubiccrystalline lattice. The cubic crystalline lattice may be that ofcalcium fluoride, in one embodiment. FIG. 3B is a 3-D plot correspondingto a quadrant of the vector plot shown in FIG. 3A, and showing thecorresponding magnitude of the intrinsic birefringence. It can be seenthat the localized magnitude and axis of the birefringence varyspatially throughout the crystal in a known fashion. It can also be seenthat, depending on the direction along which light travels through sucha cubic crystalline material, the birefringence magnitude and theorientation of the birefringence axis relative to the direction ofpropagation will vary. FIG. 3B represents an octant of the crystallattice: the extension of this diagram to all possible directionsthrough the crystal gives twelve directions for maximum birefringence,or birefringence lobes.

The crystal axis directions shown in FIGS. 3A and 3B are described usingMiller indices, which are integers with no common factors that areinversely proportional to the intercepts of the crystal planes along thecrystal axes. Lattice planes are given by the Miller indices inparentheses, e.g. (101), and axis directions in the crystal lattice aregiven in square brackets, e.g. [111]. The crystal lattice direction,e.g. [110], may also be referred to as the [110] crystal axis of theelement or material, and a cubic crystalline optical element arrangedwith its [110] crystal axis along the system optical axis, may bereferred to as a [110] optical element. The (100), (010), and (001)planes are equivalent in a cubic crystal and are collectively referredto as the {100} planes.

The crystalline material can therefore be advantageously cut along agiven plane and arranged such that light normal to that plane travelsalong a chosen axis direction. For example, light traveling along the[100] crystal axis 18 (i.e. along the [100] crystal lattice direction),which is oriented normal to the (100) crystal lattice plane 16, sees afixed and deterministic localized intrinsic birefringence. Thebirefringence magnitude and birefringence axis direction encountered bya given ray therefore varies as a function of the direction along whichthe light ray travels through the crystal.

FIG. 4 is a perspective view showing angular relationships betweenvarious directions through an exemplary cubic crystalline lattice. Thecubic crystalline lattice may be that of calcium fluoride, for example.FIG. 4 includes peak intrinsic birefringence directions along the [101],[110], and [011] lattice directions, indicated by lines 22, 24, and 26,respectively. Line 20 represents the [111] crystal axis direction, whichcorresponds to a direction through the crystal without intrinsicbirefringence.

FIGS. 5A, 5B, and 5C are schematic representations of the variations inbirefringence magnitude and birefringence axis orientation in angularspace for optical axis orientations along the [110], [100], and [111]lattice directions, respectively, for the cubic crystalline latticestructure shown in FIG. 4. The center of the plot represents thebirefringence encountered by a ray traveling along the indicated crystalaxis and normal to the plane of the illustration. Birefringence depictedat increased radial distance from the center represents thebirefringence for rays at increased angles of propagation with respectto the optical axis. In each of FIGS. 5A-5C, the localized birefringenceaxis is indicated by the direction of lines plotted on a square grid,and the magnitude is indicated by the relative length of the lines.

The variation of birefringence magnitude in FIGS. 5A-5C is characterizedby several lobes, also referred to as nodes, distributed azimuthally inwhich the birefringence is maximized. Each of FIGS. 5A-5C shows peakintrinsic birefringence lobes with respect to the various crystal axisdirections and the cubic crystalline lattice shown in FIG. 4. Thespatial orientation of the cubic crystalline lattice is indicated by theother related crystalline lattice directions indicated by the arrows.For example, in FIG. 5A in which the center represents birefringenceencountered by a ray traveling along the [110] crystal axis, a raytraveling along the [101] lattice direction is at a greater angle withrespect to the [110] crystal axis than a ray traveling along the [111]lattice direction; these ray angles are at 60° and 35.3°, respectively.This is indicated by the [101] arrowhead positioned at a greater radialdistance from center than the [111] arrowhead. The relative azimuthaldirections of the indicated [100], [101], and [111] lattice directionsare as shown in FIG. 4. This description applies to FIGS. 5B and 5C aswell.

Referring to FIGS. 5A-5C, in each case, the indicated crystal axis isthe direction normal to the plane of the figure and at the center ofeach of the respective figures. FIG. 5A shows intrinsic birefringencewith respect to the [110] lattice direction, including peak intrinsicbirefringence lobes 29A, 29B, 29C and 29D which each forms an angle of60° with respect to the [110] crystal axis direction. Intrinsic [110]birefringence also includes central birefringence node 29E. FIG. 5Bshows intrinsic birefringence with respect to the [100] latticedirection, including peak birefringence lobes 31A, 31B, 31C and 31D eachof which forms a 45° angle with respect to the [100] crystal axisdirection. There are also peaks along the diagonals at 90° not depicted.FIG. 5C shows intrinsic birefringence along the [111] lattice directionand which includes peak birefringence lobes 33A, 33B, and 33C, each ofwhich forms an angle of 35.3° with respect to the [111] crystal latticedirection.

The crystal lattice and resulting intrinsic birefringence lobes withrespect to the crystal axes such as shown in FIGS. 5A-5C, are for theexemplary embodiment in which the cubic crystals are negative cubiccrystals; that is the ordinary refractive index is greater than theextraordinary index, so the birefringence, n_(e)−n_(o), is negative.Calcium fluoride is an exemplary negative cubic crystal. For positivecubic crystals, the patterns would be substantially similar except thelines would be each rotated by 90 degrees about their midpoints. Itshould be understood that other cubic crystalline optical elements suchas barium fluoride, lithium fluoride, and strontium fluoride might beused as optical elements in other exemplary embodiments of the presentinvention. With respect to any cubic crystalline material used, thevariations in the intrinsic birefringence direction and magnitude can bemeasured, or calculated using computer modeling. Furthermore, thevariations in intrinsic birefringence direction and magnitude of anoptical material may also be measured. Graphical representations of thevariations in birefringence magnitude and axis orientations similar tothose shown in FIGS. 5A-5C, can be similarly generated for each of theaforementioned cubic crystalline materials.

Referring again to FIG. 1, it can be understood that if each ofindividual lens elements L is formed of the same cubic crystallineoptical material such as calcium fluoride and the individual lenselements L, or optical elements, are arranged along a common opticalaxis and aligned such that each of individual lens elements L that isconstructed from a cubic crystalline material, includes substantiallythe same three dimensional lattice orientation with respect to theoptical axis 10, then the net retardance of the lens system (i.e.,optical system 2) will have a retardance that varies across the systemexit pupil in a similar manner to the angular intrinsic birefringencevariation shown schematically in FIGS. 5A-5C.

Embodiment 1

FIG. 6 shows an exemplary arrangement of an optical system used todemonstrate the basic technique for mitigating the effects of intrinsicbirefringence. This exemplary optical system consists of an aberrationfree light beam converging toward a focus at a numerical aperture of0.707, giving maximum ray angles of 45° through each element. The beampasses through three cubic crystalline elements 42, 44 and 46 whoseradii of curvature are specified to be concentric with focal point 40 ofthe beam. Cubic crystalline elements 42, 44 and 46 have thicknesses 43,45 and 47, respectively. In an exemplary embodiment, each of thicknesses43, 45 and 47 may be 5 mm and cubic crystalline elements 42, 44 and 46may be assumed to have a birefringence magnitude, n_(e)−n_(o), of−12×10⁻⁷, corresponding to the intrinsic birefringence of calciumfluoride measured at a wavelength of 157 nm as suggested in D. Krahmer,“Intrinsic Birefringence in CaF₂,” at Calcium Fluoride BirefringenceWorkshop, Intl SEMATECH, Jul. 18, 2001, the contents of which are herebyincorporated by reference. In this exemplary configuration, the elementsdo not contribute wavefront aberration to the converging beam other thanretardance aberrations produced by intrinsic birefringence. For thisexample, the wavelength is 157.63 nm, and the ordinary index ofrefraction is assumed to be 1.5587.

In one exemplary embodiment, the optical system shown in FIG. 6 may bearranged such that each of elements 42, 44 and 46 are arranged along acommon optical axis and such that the three-dimensional crystal latticefor each element is aligned identically. FIGS. 7A, 7B, and 7C show howthe retardance varies over the exit pupil for cases in which the opticalaxis is along the [110], [100], and [111] lattice directions,respectively, and the three-dimensional crystal lattice for each elementis aligned identically.

FIGS. 7A, 7B and 7C are each graphical illustrations of net retardancemagnitude and orientation across the pupil for the exemplary opticalsystem shown in FIG. 6. In these plots, and the retardance pupil maps tofollow, the retardance is shown on a square grid across the system exitpupil for the optical system of interest, and is described in general byellipses which sometimes degenerate into lines that show theeigenpolarization states (i.e., the polarization state that remainsunchanged for a ray propagating through the optical system at givenpupil coordinates). The size of the ellipse or length of the line at agiven pupil coordinate is proportional to the relative strength of theretardance and the angle is related to the angle of the retardance axis.

Also, for each of the lens and corresponding retardance map embodimentsdescribed herein, the coordinates are defined using a right-handedcoordinate system such that the system optical axis is in the +Zdirection from the object towards the image plane, the +Y axis is in thevertical direction, and the +X direction is orthogonal to the Y and Zaxes. For all exit pupil retardance and wavefront maps provided herein,the plots describe variations over an exit pupil reference sphere for agiven field point using a Cartesian coordinate system, where the X and Ycoordinates are coordinates on the reference sphere projected onto aplane perpendicular to the chief ray.

Returning now to FIGS. 7A, 7B, and 7C, it can be seen that, in eachcase, the peak retardance is approximately 0.11 waves, and the RMSretardance is about 0.029 waves at a 157 nm wavelength. Thus, asignificant amount of retardance is produced for each of the opticalaxis directions through the crystal lattice in the exemplary commonlyaligned systems.

In the present invention, the crystal axes and relative rotations of theindividual elements with respect to the system optical axis are selectedsuch that the retardance produced by the intrinsic birefringence of theindividual elements combines to minimize the net retardance experiencedby light traveling through the system. The cubic crystalline opticalelements are oriented and clocked to produce a net retardance that isless than the sum of retardance produced by the intrinsic birefringenceof the respective individual cubic crystalline optical elements.

In one embodiment, the present invention provides at least three opticalelements, in which at least two of the elements are oriented with theoptical axis along their [110] crystal axes and at least one of theelements is oriented with its [100] crystal axis along the systemoptical axis.

This embodiment may be applied to the exemplary optical system shown inFIG. 6. In embodiment 1 of the present invention, the first two elements46 and 44 are oriented along the [110] cubic crystalline latticedirection and the third element 42 is oriented along the [100] latticedirection, although the specific order of the elements may be varied inother exemplary embodiments. Furthermore, the crystal lattices of the[110] first 46 and second 44 elements are rotated by 90 degrees withrespect to one another in a plane perpendicular to the optical axis.This rotation about the optical axis is known as “clocking”.

FIGS. 8A, 8B, and 8C are graphical illustrations showing the retardancemagnitude and orientation over the pupil for the individual elements inthe arrangement of the first exemplary embodiment of the optical systemshown in FIG. 6, as described above. FIGS. 8A, 8B and 8C represent theindividual retardance contributions for the first 46, second 44, andthird 42 cubic crystalline optical elements, respectively. First element46 is referred to as a [110] optical element and is oriented with its[110] crystal axis along the system optical axis, such that theretardance along the optical axis is oriented horizontally, as depictedin FIG. 8A. Second element 44 is referred to as a [110] optical elementand is oriented with its [110] crystal axis along the system opticalaxis, such that the retardance along the optical axis is orientedvertically, as depicted in FIG. 8B. Third element 42 is referred to as a[100] optical element and is oriented with its [100] crystal axis alongthe optical axis, such that the peak birefringence occurs along thepupil diagonals at azimuthal angles of ±45 degrees, as depicted in FIG.8C. Hereinafter, an optical element referred to as an [XYZ] opticalelement, is understood to be an optical element oriented with its [XYZ]lattice direction or its [XYZ] crystal axis, along the system opticalaxis.

By orienting the first two optical elements with their [110] crystalaxes along the optical axis, but rotated 90 degrees about the commonsystem optical axis with respect to one another, the horizontallyoriented retardance produced by first element 46 for light propagatingnear the optical axis may be balanced by the vertically-orientedretardance produced by second element 44. Because the retardanceorientation of the second element is orthogonal to that of the firstelement and equal in magnitude, the effect is to correct the retardanceaberration near the center of the pupil, and produce a net retardance ofessentially zero. Stated alternatively, the two individual retardancesproduced by first element 46 and second element 44, cancel each other toproduce a net retardance of essentially zero. The first two opticalelements therefore have their three-dimensional crystal lattices at afixed rotation angle about the optical axis with respect to each other.The elements are optimally clocked such that respective birefringencelobes are aligned at different three dimensional positions. Statedalternatively, the peak birefringence lobes of the first two [110]optical elements 46 and 44 are rotated with respect to each other.According to other exemplary embodiments, the [110] optical elements maybe rotated by angles other than 90 degrees and in still other exemplaryembodiments, other cubic crystalline optical elements may be used androtated or clocked about the optical axis and with respect to eachother, such that their respective three dimensional lattice directionsare not identically aligned and so as to produce a net retardance thatis reduced relative to the arrangement in which the elements have theirthree-dimensional crystal lattices aligned substantially identically.

FIG. 9A shows the net retardance of the first and second elements of thefirst exemplary embodiment of the optical system depicted in FIG. 6 andas described above. As shown, the retardance is corrected to essentiallyzero near the center of the pupil, as well as along horizontal andvertical sections bisecting the pupil. Residual retardance is noted,however, along the pupil diagonals, and is oriented at roughly ±45degrees, directed towards the center of the pupil.

Returning to FIG. 8C, the retardance produced by third element 42 of thefirst exemplary embodiment of the optical system depicted in FIG. 6oriented with its [100] crystal axis along the optical axis, has peakretardance along the diagonals of the pupil, but the magnitude of theretardance is opposite in sign to the net retardance produced by thefirst and second elements 46 and 44, as shown graphically in FIG. 9A. Inthe exemplary embodiment, the [100] optical element is rotated about thecommon optical axis such that the peak birefringence lobes are rotatedsubstantially by 45° with respect to the directions of the localbirefringence axes along the [110] crystal axes of the two, 90° clocked[110] optical elements. It can therefore be seen that the retardanceorientation for the contribution of the third element (FIG. 8C) isapproximately orthogonal to the net contribution from the first andsecond elements (FIG. 9A).

FIG. 9A shows that two [110] optical elements at 90 degree relativerotations about the optical axis, produce a residual retardance erroralong the diagonals, but provide for corrected retardance alonghorizontal and vertical slices through the center of the pupil. Usingthe same principles, a [100] optical element may be used to furtherreduce the overall retardance.

FIG. 9B shows net retardance due to the contributions from all threeelements of the first exemplary embodiment of the optical systemdepicted in FIG. 6. It should be understood that the [100] opticalelement may be either first element 46, second element 44 or thirdelement 42, with essentially the same result. The residual netretardance is oriented roughly azimuthally and increases from zero atthe center of the pupil to a peak at the edge of the pupil. The peakretardance is approximately 0.019 waves, and the RMS retardance over thepupil is approximately 0.005 waves. In comparison to the uncorrectedbirefringence shown in FIGS. 7A, 7B and 7C, each having a peakretardance of approximately 0.11 waves and a RMS retardance ofapproximately 0.029 waves, it can be understood that the peak retardancehas been reduced by a factor of roughly six.

According to another exemplary embodiment in which thickness 43 of thirdelement 42 is about 2.3 mm, the peak retardance may be reduced to 0.0139waves, with an RMS retardance of 0.0041 waves. This retardance is shownin FIG. 9C. According to this exemplary embodiment, the peak retardancewas reduced by a factor of approximately eight. According to otherexemplary embodiments, other thicknesses may be used for elements 42, 44and 46 to yield different retardance values.

According to another exemplary embodiment, the residual error in FIG. 9Bmay be further reduced by a birefringent element that producesradially-oriented retardance that increases in magnitude from the centerto the edge of the component. Such an element may be produced byapplying a hoop stress to the edge of a meniscus optical component andadded to the exemplary optical system of the first embodiment and asshown in FIG. 6. The applied stress creates a spatially varyingbirefringence to compensate for the computed or measured birefringencevariation within the optical system as shown in FIG. 9B. Variousstresses may be applied to various optical elements to achieve thespatially varying birefringence. The stressed optical element may be alens element or a window and aligned along the optical axis. Varioustechniques may be used to apply the stress.

FIG. 9D shows the spatial radial retardance variation induced byapplying an exemplary compressive hoop stress of 1000 pounds per squareinch to first element 46 of FIG. 6. In this exemplary embodiment,element 46 has radii of curvature of 40 and 35 mm and a centralthickness of 5 mm. Differently shaped elements will have differentradial retardance variations, which can be used to substantially cancelthe retardance contributions such as those shown in FIG. 9B. The stressinduced birefringence varies spatially over the element, which isfundamentally different than retardance from intrinsic birefringencethat varies as a function of the angle of a ray with respect to thecrystal axis. This provides another important tool for reduction ofsystem retardance.

According to the exemplary embodiment illustrated in FIG. 6, in whichthe first two elements 46 and 44 are [110] cubic crystalline opticalelements, third element 42 is a [100] cubic crystalline optical element,and all elements are 5 mm thick, first element 46 may include a tensilehoop stress of approximately 24 lbs./in² applied around the perimeter tominimize the net RMS retardance. The relative crystal latticeorientations for optical elements 42, 44 and 46 are as described above.

FIG. 9E is a graphical representation depicting the individualretardance contribution due to the stress-induced birefringence of firstelement 46 shown in FIG. 6. FIG. 9E shows the individual contribution tothe retardance across the pupil for first element 46, when a tensilehoop stress of approximately 24 lbs./in² is applied around the perimeterof the element, and does not include the retardance caused by intrinsicbirefringence. FIG. 9E indicates a peak retardance of 0.0170 waves andRMS retardance of 0.0055 waves. In this exemplary embodiment, theradially oriented retardance produced by the stress element compensatesfor the residual retardance for the embodiment without stress-inducedbirefringence depicted in FIG. 9B.

FIG. 9F is a graphical illustration showing the net retardance acrossthe pupil for the exemplary embodiment including the stress-inducedbirefringence of first element 46. With a tensile stress ofapproximately 24 lbs./in² applied to first element 46, the maximumresidual retardance is 0.0073 waves, and the RMS retardance is 0.0024waves for the optical system. This represents a significant improvementover the respective peak and RMS retardance values of 0.019 and 0.005waves, respectively, that result without applying stress-inducedbirefringence to first element 46, as shown in FIG. 9B. The appliedstress is intended to be exemplary only and various other appliedstresses of different magnitudes, may be used depending on the residualretardance of the system which, in turn, depends on the number and typesof cubic crystalline optical elements, the orientation and thickness ofthe optical elements, and the like.

According to yet another exemplary embodiment in which the first twoelements 46 and 44 are [110] cubic crystalline optical elements andthird element 42 is a non-cubic crystalline, non-birefringent element, atensile hoop stress may be applied around the perimeter of third element42 to minimize the net RMS retardance using the principles as above.Various stress values may be applied.

Another aspect of the present invention is the method for measuring orusing computer modeling to determine the retardance of an opticalsystem, identifying an optical element or elements to havestress-induced birefringence applied thereto, then applying thecompressive or tensile stress as a hoop or other stress, to producestress-induced birefringence as described above, to reduce residualretardance.

According to other exemplary embodiments having a residual retardancethat is constant, or which varies after correction, various birefringentelements may be added to correct for the residual retardance. In anexemplary embodiment, a wave plate may be added to the system to correctfor constant retardance; this wave plate may constructed from stressinga parallel plate. According to other exemplary embodiments, a poweredbirefringent element having constant birefringence magnitude may be usedto compensate for residual variations in retardance. The powered elementmay be a uniaxial crystalline material or it may include astress-induced birefringence, as above. Other optical elements withstress-induced birefringence may additionally or alternatively be usedto correct for residual retardance variation. The various exemplaryoptical elements may include a stress that varies linearly across theelement or quadratically in the radial direction, along an axissubstantially orthogonal to the optical axis. The birefringent elementor elements will be chosen and positioned to correct for the constant orvarying retardance residual in the system after correction as above.

Embodiment 2

According exemplary embodiment 2, the present invention provides anapparatus that achieves reduced retardance through the use of at leastfour [110] optical elements and at least one [100] optical element. Inthe illustrated embodiment shown in FIG. 10, the present inventionprovides an apparatus having four elements with their [110] crystal axesalong the system optical axis and one element with its [100] crystalaxis along the system optical axis.

The relative orientations of the lattice directions in the planeperpendicular to the optical axis may be adjusted for the [110] opticalelements. This technique is known as “clocking” or rotating the crystallattice orientation of elements aligned along a common optical axis. Therelative orientations may be selected in a particular manner thatrelates to the azimuthal orientations of the off-axis peak birefringencelobes.

Referring to FIG. 4, there are peak birefringence lobes at 60° withrespect to the [110] crystal axis, corresponding to the [011] and [101]directions (as well as two additional lobes not shown in FIG. 4).

FIG. 5A shows a retardance pupil map for a [110] optical element. Asshown, the four outer birefringence lobes are not distributed by equalazimuthal angles. If the crystal lattice is defined to give horizontallyoriented retardance along the optical axis for a negative birefringencemagnitude, n_(e)−n_(o), the peaks are at azimuthal angles of ±35.26° and±144.74°.

FIG. 10 shows an optical system according to the second exemplaryembodiment. This exemplary five-element optical system consists of anaberration-free light beam converging toward a focus 50 at a numericalaperture of 0.707, giving maximum ray angles of 45° through eachelement. Cubic crystalline optical elements 52, 54, 56, 58 and 60 arealigned along optical axis 51. A light beam passes through five cubiccrystalline elements 52, 54, 56, 58 and 60 whose radii of curvature areeach concentric with the focal point 50 of the beam. In an exemplaryembodiment, the elements each have thicknesses of about 2.5 mm, and areassumed to have a birefringence magnitude each, n_(e)−n_(o), of−12×10⁻⁷, corresponding to the intrinsic birefringence of calciumfluoride measured at a wavelength of 157 nm. According to otherexemplary embodiments, other thicknesses may be used. In thisconfiguration, the elements do not contribute wavefront aberration tothe converging beam, other than retardance aberrations produced byintrinsic birefringence. According to an exemplary embodiment, thewavelength of light may be 157.63 nm, and the ordinary index ofrefraction may be 1.5587. Other wavelengths and indices of refractionmay be used in other exemplary embodiments.

FIGS. 11A, 11B, and 11C are graphical representations showing how theretardance varies over the exit pupil for cases in which each ofelements 52, 54, 56, 58 and 60 of FIG. 10 are [110], [100], and [111]optical elements, respectively, and the three-dimensional lattice foreach element is aligned identically. In each case, the peak retardanceis approximately 0.095 waves, and the RMS retardance is about 0.024waves at the indicated wavelength of 157 nm. Thus, a significant amountof retardance is produced for each of the optical axis directionsthrough the crystal lattice.

According to the second exemplary embodiment, as applied to theexemplary optical system depicted in FIG. 10, the first four elements52, 54, 56 and 58 are oriented with their [110] crystal axes alongoptical axis 51 and fifth element 60 is oriented with its [100] crystalaxes along optical axis 51. According to other exemplary embodiments,the specific order of the components may be changed. According to thissecond exemplary embodiment, the relative clockings of the four elements52, 54, 56 and 58 with optical axes along the [110] direction, may be,in order, 17.632°, −17.632°, 72.368°, and −72.3680. Fifth [100] element60 is oriented such that the peak birefringence lobes are at azimuthalangles of ±45°.

FIGS. 12A to 12D show the retardance maps for the individual elementcontributions for the four [110] optical elements in which the fourelements are clocked as described above.

Relative to an element clocking that provides horizontally orientedretardance along the optical axis, first element 52 is rotated by17.632°, which locates the peak birefringence lobes at azimuthal anglesof 52.897°, 162.368°, −17.632°, and −127.104°. The retardance map forthe retardance contribution from first element 52 is shown in FIG. 12A.

FIG. 12B shows the retardance contribution of second element 54, whichis rotated by −17.632° to position the peak birefringence lobes atazimuthal angles of 17.632°, 127.104°, −52.897°, and −162.368°.

FIG. 12C shows the retardance contribution of third element 56, which isrotated by −72.368° to position the peak birefringence lobes atazimuthal angles of 107.632°, 37.104°, −72.368°, and −142.896°.

FIG. 12D shows the retardance contribution of fourth element 58, whichis rotated by −72.368° to position the peak birefringence lobes atazimuthal angles of 72.368°, 142.896, −37.104°, and −107.632°. Therelative clockings of the four elements with optical axes along the[110] lattice direction are related to half of the azimuthal angle shownin FIG. 5A, i.e. ±17.632° or ±(90−17.632)°.

As shown in FIGS. 12A and 12D, the retardance contribution of firstelement 52 is orthogonal to that of fourth element 58 near the center 61of the pupil. Similarly, FIGS. 12B and 12C show that the retardancecontribution of second element 54 is orthogonal to that of third element56 near the center 61 of the pupil.

FIG. 13A shows the individual retardance contributions of the first andthird elements 52 and 56 overlapping one another. Over central portion62 of the pupil, the retardance orientations are crossed at an averageangle of roughly 45°. At positions 64 along the outer edge of the pupiland along the −45° diagonal, the retardance orientations are the same.

FIG. 13B shows the net retardance for the combination of first element52 and third element 56. Over a wide region of the pupil along the 45°diagonal, the retardance is oriented at a 45° angle. At the edge of thepupil along the −45° diagonal, the retardance is oriented at −45°.Similarly, FIG. 13C shows the net retardance of second element 54 andfourth element 58, which gives a retardance orientation over the pupilthat is roughly orthogonal to the net retardance of the first and thirdelements as shown in FIG. 13B.

FIG. 14A shows the net retardance for the four elements 52, 54, 56 and58 with their respective [110] crystal axes along optical axis 51, andoriented as described above. The maximum retardance is 0.0181 waves andthe RMS retardance is 0.0049 waves, which is a reduction in retardanceof roughly a factor of five compared with all of the element crystallattices aligned identically in three dimensions as depicted in FIGS.11A, 11B and 11C. The residual retardance orientation is radial withlarger retardance magnitude along the ±45° diagonals.

The retardance contribution for fifth element 60, which is oriented tohave its [100] lattice direction along the optical axis, is shown inFIG. 14B. As shown, the retardance is similar in magnitude to theresidual net retardance of the first four elements 52, 54, 56 and 58shown in FIG. 14A, and the orientation is generally perpendicular acrossthe pupil. This allows for nearly perfect correction or canceling of theretardance. According to the second exemplary embodiment in which thefirst four [110] optical elements 52, 54, 56 and 58 are aligned alongoptical axis 51 and have a net retardance shown in FIG. 14A and in whichthe fifth optical element 60 is aligned to have its [100] crystal axisalong optical axis 51, the net retardance for all five elements has amaximum of about 0.0007 waves and RMS retardance of 0.0002 waves asshown in FIG. 14C.

The second exemplary embodiment thus shows that four [110] opticalelements and one [100] optical element with identical thicknesses andray angles are aligned to reduce the peak retardance from 0.0952 waveswhen all elements are identically oriented [110] elements, to a peak of0.0007 waves, and the RMS retardance is reduced from 0.0229 waves to0.0002 waves, a reduction by a factor of more than 100 in both cases.

It should be understood that the first embodiment with two [110] opticalelements and one [100] optical element, and the second embodiment withfour [110] optical elements and one [100] optical element, are exemplaryonly and that various numbers of optical elements may be used andclocked, in accordance with the preceding principles to balance theindividual intrinsic birefringence contributions of the elements andproduce a reduced net birefringence and retardance. These principles maybe applied to lens systems, including cubic crystalline lens elementsexclusively or they may be applied to lens systems including cubiccrystalline and other lens elements.

Also as described in conjunction with embodiment 1, one or more stressbirefringent elements, wave plates, or combinations thereof mayadditionally be used to correct for residual birefringence variation andconstant residual retardance which remains after the above-describedsystem corrections have been made.

Concepts of the Invention

The basic principles used to compensate the effects of intrinsicbirefringence, as applied to the first and second exemplary embodimentscorresponding to the exemplary lens arrangements shown in FIGS. 6 and10, respectively, can be extended to compensate for the effects ofintrinsic birefringence effects in various other high-performance, highnumerical aperture optical systems, such as those used forphotolithography in other exemplary embodiments. The principles applyboth to refractive and catadioptric lens systems and may be used whendesigning new lens systems or to improve a known lens prescription.

According to other exemplary refractive and catadioptric lens systems,the individual lens element thicknesses, radii of curvature, asphericcoefficients, and ray angles may differ significantly from component tocomponent. Additional non-cubic crystalline lens elements may optionallybe included. Nonetheless, it will be shown in the embodiments to followas in the previous embodiments, that the crystal orientation andrelative clockings of the components may be chosen to reducebirefringence and therefore retardance. The illustrated embodiments showoptical elements having their [110] crystal axes along the optical axis,used in conjunction with optical elements having their [100] crystalaxes along the optical axis to balance, or cancel retardance aberrationsproduced by intrinsic birefringence. A general concept of the presentinvention is to provide an optical system which includes a projectionlens formed of a plurality of optical elements, two or more of which areconstructed from cubic crystalline material and oriented with their[110] cubic crystalline lattice direction along the system optical axisand with relative rotations about the optical axis to give reducedretardance for light propagating at small angles relative to the systemoptical axis, and one or more elements oriented with the optical axissubstantially along the [100] cubic crystalline lattice direction togive reduced retardance for light propagating at larger angles withrespect to the system optical axis, that is, locations off the opticalaxis.

In other embodiments, an element or elements having their [111] crystalaxes aligned along the optical axis, as shown in FIG. 5C, may be used inconjunction with other element combinations to substantially cancel theretardance throughout the field using the same principles described forthe [110] and [100] embodiments. In various exemplary embodiments, lensdesign software may be used to generate the lens prescription includingpositioning of the individual lens elements, as well as thicknesses,radii of curvature, aspheric coefficients and the like. In oneembodiment, the RMS retardance may be computed over a pupil grid at eachfield point and used as the merit function for a damped least squaresoptimization using the commercially available lens software, CODE V, forexample. A computer may be used to optimize the orientation and clockingof each of the elements in the system.

Phase aberrations, such as astigmatism, introduced by the average indexvariations in the cubic crystalline elements, may be compensated usingone or more surfaces with different radii of curvature along orthogonaldirections. The variation in average index of refraction produced by[100] optical elements is generally more easily compensated than thevariation produced by [110] optical elements, due to a more gradualvariation in average index of refraction as a function of propagationangle with respect to the optical axis. Therefore, a sufficiently highnumber of [100] optical lens elements may advantageously be used alongthe optical axis to minimize high-order variations in average index ofrefraction.

According to other exemplary embodiments, the thicknesses of thecomponents, the spacings between the components, and the radii ofcurvature and aspheric coefficients of the lens elements, may similarlybe optimized to balance aberrations and reduce retardance across thefield. According to yet another exemplary embodiment, the cubiccrystalline lens elements may be selected and positioned such thatelements having a birefringence magnitude that is opposite in sign toanother lens element or elements, may be used together to substantiallycancel retardance produced by intrinsic birefringence and produce a netretardance of near zero throughout the field. For example, a calciumfluoride lens element (having a negative birefringence magnitude) may beused in conjunction with a barium fluoride lens element (having apositive birefringence magnitude) and aligned along the same crystallattice direction, so that the retardance throughout the field issubstantially cancelled.

The third, fourth and fifth embodiments are based on lens prescriptionspublished in the art. Such are intended to be exemplary only and theprinciples and concepts of the present invention may be applied to anyof various other lens arrangements. Application of the present inventionis of particular interest for high numerical aperture optical systemsfor photolithography at an exposure wavelength near 157 nm, such as thatproduced by an F₂ excimer laser. Because many of the available opticalsystems described in the art include lower numerical apertures andoperate at longer wavelengths such as 193 nm, the techniques of thepresent invention are illustrated by application to exemplary knownoptical systems designed for an exposure wavelength near 193 nm,corresponding to the wavelength produced by an ArF excimer laser,commonly used in photolithography. It should be understood, however,that the principles and techniques of the present invention applyequally to high numerical aperture systems and systems operating at 157nm.

To estimate the effects of intrinsic birefringence in high numericalaperture lenses designed for a central wavelength of 157 nm, in whichthe refractive elements are primarily constructed from calcium fluoride,each element in the following embodiments, which may be constructed fromfused silica or calcium fluoride in the various embodiments, is assumedto have a peak intrinsic birefringence of (n_(e)−n₀)=−12×10⁻⁷, which isroughly equivalent to the measured peak intrinsic birefringence incalcium fluoride at a wavelength of 157 nm.

In this manner, the method for compensation of intrinsic birefringencein similar high numerical aperture lenses designed for 157 nm may bedemonstrated using known exemplary lens descriptions designed for acentral wavelength of 193 nm as starting points. The change in centralwavelength may result in a change in refractive index of the refractivecomponents and may warrant the use of fluoride materials such as calciumfluoride, but the types of elements used and distributions of ray anglesfor a given numerical aperture are similar enough to allow a lensdesigned for a central wavelength of 193 nm to be used to demonstratethe inventive techniques for mitigating the effects of intrinsicbirefringence in high numerical aperture lenses, particularly at acentral wavelength of 157 nm.

In the descriptions of embodiments 3, 4 and 5 that follow, eachrefractive surface is assumed to have a hypothetical, single layeranti-reflection coating with an index of refraction equal to the squareroot of the element index of refraction and with an optical thickness ofa quarter wave at a wavelength of 193.3 nm. The indices of refractionfor calcium fluoride and fused silica used in each of the embodimentsare assumed to be 1.501455 and 1.560326, respectively, at a wavelengthof 193.3 nm. Different coatings will introduce different retardance andphase aberrations and will require slightly different compensation. Itshould be understood, however, that the method demonstrated for thesingle hypothetical coating is applicable to systems with various otherphysical coatings.

In each of embodiments 3-5 that follow, the corrected optical system isbased on a given lens prescription. The given lens prescription may bemaintained and the effects of intrinsic birefringence compensated for,using the techniques described above, and additionally or alternativelyby the splitting of one or more lens elements of the given prescription,into two or more sub-elements. The principles of the present inventionmay, however, be advantageously be applied to various other new lensprescriptions being designed, with the advantages of the presentinvention incorporated into the lens design.

Furthermore, one or more birefringent elements, wave plates, orcombinations thereof as described in conjunction with embodiments 1 and2, may additionally be used to correct for residual birefringencevariation and constant residual retardance after the describedcorrections have been made to the systems as described in embodiments 3,4 and 5.

Embodiment 3

The third exemplary embodiment for application of the compensationtechniques for intrinsic birefringence may be described in conjunctionwith an exemplary all-refractive projection lens used forphotolithography. Such an exemplary lens is provided in the fifthembodiment of European Patent No. 1 139 138 by Y. Omura, the contents ofwhich are herein incorporated by reference. This exemplary lens isdepicted in the schematic illustration of FIG. 15. This exemplary systemis designed to operate at a central wavelength of 193.3 nanometers,provides 4× reduction at a numerical aperture of 0.75, and has an imagefield diameter of 27.5 mm. The exemplary design employs 20 elements Ewith six aspheric surfaces constructed from calcium fluoride and fusedsilica; however, each component is assumed to have an intrinsicbirefringence of −12×10⁻⁷ in the following baseline computations. Theexemplary system includes optical axis 65.

The RMS and maximum retardance and diattenuation over the exit pupil arelisted in Table 1 below for the nominal design without intrinsicbirefringence effects included for relative field heights of 0, 0.7, and1.0. The relative field height is defined to be the actual field heightnormalized by the semi-field height. Thus, an image located on theoptical axis has zero field height and an image located at 13.75 mm inthis lens corresponds to unit relative field height. The retardance anddiattenuation result from the single-layer anti-reflection coatings usedin the model. FIGS. 16A and 16B depict the retardance across the systemexit pupil due to the anti-reflection coatings for the field points atthe center and edge of the field, respectively. The retardance isradially-oriented and is largest in magnitude at the edge of the pupil.The retardance due only to the anti-reflective coating is relativelysmall.

TABLE 1 Retardance Relative Field (waves at λ_(o) = 193.3 nm)Diattenuation Height RMS Maximum RMS Maximum 0.0 0.0033 0.0125 0.00530.0217 0.7 0.0034 0.0132 0.0053 0.0230 1.0 0.0035 0.0149 0.0057 0.0247

FIGS. 17A and 17B show the diattenuation variation across the pupil forthe center and edge of the field, respectively, for the optical systemillustrated in FIG. 15. Diattenuation may be described as a measure ofthe maximum difference in transmission between orthogonal polarizationstates.

The RMS and peak-to-valley wavefront error are listed in Table 2 belowfor the nominal design, without the effects of intrinsic birefringence.The wavefront errors are given for relative field heights of 0, 0.7, and1.0 in the Y direction, and are listed for two orthogonal polarizationcomponents. The X component represents the wavefront error for an inputpolarization in the X direction assuming a linear polarizer along the Xdirection at the system exit pupil. The Y component represents thewavefront error for an input polarization in the Y direction assuming alinear polarizer along the Y direction at the exit pupil. As shown, thenominal design includes a peak RMS wavefront error of about 0.003 waves.

TABLE 2 Peak-to-Valley RMS Wavefront Error Wavefront Error (waves atλ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) Relative Field X Y X YHeight Component Component Component Component 0.0 0.002 0.002 0.0120.012 0.7 0.003 0.002 0.020 0.020 1.0 0.003 0.002 0.018 0.012

In FIGS. 18A, 18B, 18C, and 18D, wavefront errors at a wavelength of193.3 nm are plotted at the system exit pupil as contour maps. FIGS. 18Aand 18B show contour plots of the residual wavefront error for the lensdepicted in FIG. 15 corresponding to an input polarization in the Xdirection (perpendicular to the field height) used with an exit pupilanalyzer in the X direction for the central and extreme field points,respectively. For the wavefront error at the central field point shownin FIG. 18A, the maximum peak-to-valley optical path difference is 0.012waves, and for the wavefront error at the extreme field shown in FIG.18B, the maximum peak-to-valley optical path difference is approximately0.018 waves. FIGS. 18C and 18D show contour plots of the residualwavefront error for the lens depicted in FIG. 15 corresponding to aninput polarization in the Y direction (parallel to the field height)used with an exit pupil analyzer in the Y direction for the central andextreme field points, respectively. For the wavefront error at each ofthe central and extreme field points shown in FIGS. 18C and 18D,respectively, the maximum peak-to-valley optical path difference isapproximately 0.012 waves.

The centroid distortion for the nominal design, calculated based on thepoint spread function, and the telecentricity error in the Y directionare listed in Table 3 below at relative field heights of 0, 0.7, and1.0.

TABLE 3 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.00 4.05 0.28 1.0 0.00 3.45 1.28When the effects of intrinsic birefringence associated with the cubiccrystalline lens material are taken into account, system performancedegrades significantly. FIGS. 19A and 19B are graphical illustrationsshowing the net retardance across the system exit pupil for field pointsat the center and edge of the field, respectively, according to thearbitrarily designated exemplary embodiment in which all lens elementsE, shown in FIG. 15, are identically aligned in three dimensions, withthe elements having their [110] crystal axis along optical axis 65.FIGS. 19A and 19B include the effects of intrinsic birefringence. Theobject field height in FIG. 19A is 0 mm and the object field height inFIG. 19B is 55 mm, corresponding to the center and edge field points,respectively. In the retardance pupil maps given in FIGS. 19A and 19B,and in others to follow in which the net retardance exceeds a magnitudeof 0.5 waves, the retardance is plotted “modulo 0.5 waves.” It cantherefore be seen that the retardance orientation rotates by 90 degreesat one-half-wave intervals, i.e., the effect of a 0.75 wave retarder at0 degrees is the same as a 0.25 wave retarder at 90 degrees. Thus, thepeak retardance due to intrinsic birefringence in this exemplaryarrangement is approximately 1.5 waves at a wavelength of 193.3nanometers, with small variation with object field height.

FIGS. 20A and 20B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem shown in FIG. 15. In FIGS. 20A and 20B, the net retardance acrossthe system exit pupil, including the effects of intrinsic birefringence,is depicted for field points at the center and edge of the field withall elements arbitrarily aligned identically in three dimensions, withtheir [100] crystal axes along the optical axis. Again, the retardanceorientation rotates by 90 degrees at one-half-wave intervals; thus, thepeak retardance due to intrinsic birefringence in this example isapproximately 0.9 waves at a wavelength of 193.3 nanometers.

FIGS. 21A and 21B are graphical illustrations of the retardance ofanother exemplary embodiment of crystal lattice orientation of the lenssystem shown in FIG. 15. In FIGS. 21A and 21B, the net retardance acrossthe system exit pupil is depicted for field points at the center andedge of the field with all elements arbitrarily aligned identically inthree dimensions, for [111] optical elements. In this exemplaryarrangement, the peak retardance due to intrinsic birefringence isapproximately 0.5 waves at a wavelength of 193.3 nanometers, and thevariation with field height is small.

Each of three preceding examples, as illustrated in FIGS. 19A-21C, showsthat the intrinsic birefringence produces very large retardanceaberrations and consequently large wavefront aberrations, when each ofthe elements are oriented identically with respect to the optical axis.Without compensation, this aberration strongly exceeds the allowablewavefront error for photolithography.

In the present embodiment of the present invention, the variables usedfor compensation of the retardance produced by the intrinsicbirefringence described above are the orientations of the crystal axisfor each element with respect to the optical axis and the relativerotations of those elements about the optical axis. The rotation of alens element with rotationally symmetric surfaces about its optical axisis sometimes referred to as element ‘clocking.’

One aspect of the present invention is the use of at least two [110]optical elements and at least one [100] optical element aligned along anoptical axis. This allows the retardance contributions of the individualelements to be balanced to provide wavefront correction and reduce thenet retardance produced by the intrinsic birefringence to a level thatis acceptable for high numerical aperture lithography systems. This wasdescribed in the first embodiment and is also applicable to embodiment3, as will be shown.

FIG. 22 shows the third embodiment of the present invention as appliedto the optical system previously shown in FIG. 15. FIG. 22 is aschematic, side view of the lens. In this embodiment, elements E1, E5,E6, E13, E14, E15, and E18, numbered with respect to the object plane70, are aligned with their [100] crystal axes along optical axis 75, andall other elements E are aligned with their [110] crystal axes alongoptical axis 75. In FIG. 22, each of the [100] optical elements (E1, E5,E6, E13, E14, E15 and E18) is hatched.

The directions of the crystal lattices and clockings of each of thecomponents are given in Table 4 below for the third exemplaryembodiment. For [110] optical elements oriented with their [110] opticalaxis along optical axis 75, the clocking of each element is givenrelative to an orientation that produces peak birefringence along theoptical axis that is oriented with the retardance axis substantiallyparallel to the X axis (horizontal, in the direction perpendicular tothe specified field of view). For [100] optical elements oriented withtheir [100] crystal axis along optical axis 75, the clocking of eachelement is given relative to an orientation that produces peakbirefringence lobes in the X-Z and Y-Z planes (at radial angles of 0,90, 180, and 270 degrees). It should be understood that such isexemplary only and the relative clocking of the elements may bedescribed with respect to any of various arbitrary reference locations.

TABLE 4 Crystal Axis along Optical Element Clocking Element Axis(degrees) E1 [100] 14.20 E2 [110] −45.84 E3 [110] 35.47 E4 [110] −52.88E5 [100] 28.30 E6 [100] 28.69 E7 [110] 72.03 E8 [110] −28.62 E9 [110]63.44 E10 [110] 5.06 E11 [110] 79.87 E12 [110] 5.73 E13 [100] 30.26 E13,Surface S2 — −52.00 E14 [100] 10.01 E15 [100] 15.09 E16 [110] −26.15 E17[110] −105.71 E18 [100] 1.69 E19 [110] 145.51 E20 [110] 35.55 Image —0.0000133

The net intrinsic birefringence of the system is significantly reducedas a result of the element orientation as shown in Table 4.

Another effect produced by intrinsic birefringence in the cubic crystallattice is variation of the average index of refraction as a function ofray angle through the cubic crystalline material. After compensation ofthe retardance errors resulting from intrinsic birefringence as above,the residual wavefront aberrations and distortion resulting from thevariations in average index of refraction may desirably also becompensated. This variation in average index of refraction typicallyproduces astigmatism in the wavefront and may result in distortion ofthe image that may be balanced in the optical design. This distortionmay include image shift, image rotation, magnification error, or higherorder distortion.

In this third exemplary embodiment, further modifications made to theoptical design compensate for the effects of variations in average indexof refraction. Surface S2 of element E13, the surface immediatelypreceding aperture stop 72, is non-rotationally symmetric or includes anasymmetric variation in curvature. In the exemplary embodiment, surfaceS2 of element E13 is a toroidal surface in which the radius of curvaturein orthogonal directions varies along with the clocking of the surface.Table 5 shows that the radius of curvature for S2 in the local Xdirection differs from that in the local Y direction. The radii ofcurvature of the last seven surfaces are adjusted to balance residualdistortion, and the image plane rotated to remove residual imagerotation. The revised radii of curvature are listed in Table 5 below,and the image plane rotation is given in Table 4 above. Although thenon-rotationally symmetric element is a [100] optical element in theexemplary embodiment, the toroidal or other non-rotationally symmetricsurface may be used on other cubic crystalline or non-cubic crystallineoptical elements in other exemplary embodiments. In various exemplaryembodiments, an optical element may include a pair of surfaces that eachhave an asymmetric variation in curvature.

TABLE 5 Surface Radius of Curvature (mm) E13, Surface S2, local Xdirection −913.123746 E13, Surface S2, local Y direction −913.128860E17, Surface S1 179.985780 E17, Surface S2 309.315227 E18, Surface S1150.015302 E18, Surface S2 225.037081 E19, Surface S1 114.371026 E19,Surface S2 390.970966 E20, Surface S1 −7083.652132 E20, Surface S2Infinite

An aspect of the present invention is that the retardance compensationthat may be achieved in a high-performance optical system is relativelyinsensitive to changes in ray angles through the components within thefield of view. Referring to FIG. 4, the outer peak birefringence lobesare each at a 600 angle with respect to the [110] crystal axis. Thisangle is particularly large compared with the corresponding angles of45° and 35.260 for the [100] and [111] crystal axes, respectively, alsoshown in FIG. 4. Thus, selecting the [110] crystal axis for asubstantial number of components allows retardance correction over alarge field of view.

FIGS. 23A and 23B are graphical representations that depict theretardance across the system exit pupil for the compensated systemdetailed above and described in Tables 4 and 5. The retardance is causedby the intrinsic birefringence and anti-reflection coatings. Aspreviously shown in FIGS. 16A and 16B, the contribution due the coatingsis relatively small; thus, the bulk of the retardance aberration is dueto the intrinsic birefringence. FIG. 23A shows retardance at the centerfield point and FIG. 23B shows retardance at the edge field point.

The RMS and maximum retardance over the exit pupil are listed in Table 6below for relative field heights of 0, 0.7, and 1.0. These include theeffects of intrinsic birefringence and the single layer anti-reflectioncoatings used in the model. A relative field height of 0.0 correspondsto the center field point shown graphically in FIG. 23A, and a relativefield height of 1.0 corresponds to the edge field point showngraphically in FIG. 23B. The RMS retardance ranges from 0.0086 to 0.0105waves at λ₀=193.3 nm.

TABLE 6 Retardance (waves at λ_(o) = 193.3 nm) Relative Field Height RMSMaximum 0.0 0.0086 0.0524 0.7 0.0093 0.0529 1.0 0.0105 0.0597

The RMS and peak-to-valley wavefront error for the exemplary correctedsystem of the third embodiment are listed in Table 7 below for thecompensated design that includes the effects of intrinsic birefringence.These data are shown graphically for relative field heights of 0.0 and1.0 in FIGS. 23A and 23B, respectively. The wavefront errors are givenfor relative field heights of 0, 0.7, and 1.0 in the Y direction, andare listed for two orthogonal polarization components. The X componentrepresents the wavefront error for an input polarization in the Xdirection assuming a linear polarizer along the X direction at thesystem exit pupil. The Y component represents the wavefront error for aninput polarization in the Y direction assuming a linear polarizer alongthe Y direction at the exit pupil. With the effects of intrinsicbirefringence included, an RMS wavefront error that varies from 0.008 to0.010 waves across the field has been achieved due to the correctiontechnique. The peak-to-valley wavefront error has been reduced by afactor of about 27, compared with alignment of all elements along the[110] lattice direction. Thus, this embodiment demonstrates thatintrinsic birefringence effects can be reduced to a level acceptable forhigh numerical aperture lithography.

TABLE 7 Peak-to-Valley RMS Wavefront Error Wavefront Error (waves atλ_(o) = 193.3 nm) (waves at λ_(o) = 193.3 nm) Relative Field X Y X YHeight Component Component Component Component 0.0 0.009 0.010 0.0570.041 0.7 0.008 0.009 0.056 0.046 1.0 0.008 0.010 0.051 0.055

FIGS. 24A, 24B, 24C, and 24D show wavefront errors plotted at the systemexit pupil as contour maps. FIGS. 24A and 24B show contour plots of theresidual wavefront error for the exemplary lens depicted in FIG. 22corresponding to an input polarization in the X direction (perpendicularto the field height) used with an exit pupil analyzer in the X directionfor the central and extreme field points, respectively. For thewavefront error at the central field point shown in FIG. 24A, themaximum peak-to-valley optical path difference is approximately 0.057waves at a wavelength of 193.3 nanometers, and for wavefront error atthe at the extreme field shown in FIG. 24B, the maximum peak-to-valleyoptical path difference is approximately 0.051 waves. FIGS. 24C and 24Dshow contour plots of the residual wavefront error for the lens depictedin FIG. 22 corresponding to an input polarization in the Y direction(parallel to the field height) used with an exit pupil analyzer in the Ydirection for the central and extreme field points, respectively. Forthe wavefront error at the central field point shown in FIG. 24C, themaximum peak-to-valley optical path difference is approximately 0.041waves at a wavelength of 193.3 nanometers, and for the wavefront errorat the extreme field shown in FIG. 24D, the maximum peak-to-valleyoptical path difference is approximately 0.055 waves.

The centroid distortion for the compensated design with intrinsicbirefringence, calculated based on the point spread function, and thetelecentricity error in the Y direction are listed at relative fieldheights of 0, 0.7, and 1.0 in Table 8 below. Telecentricity errors aredeviations from normal incidence of the cone of rays at the image plane.As shown, the residual distortion in the X and Y directions is wellwithin 0.1 nm, which is suitable for 157 nm lithography. The distortionhas also been significantly reduced relative to distortion for thenominal design described in Table 3. Changes in telecentricity errorfrom the nominal design are negligible.

TABLE 8 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 −0.06 −0.05 0.28 1.0 0.08 −0.05 1.28

Table 9 provides a summary of the performance of the design in terms ofthe Strehl ratio. The Strehl ratio describes the peak intensity of thepoint spread function relative to that of an aberration-free system. Theeffects of polarization and apodization are included in thiscalculation, as well as wavefront aberrations. At high numericalaperture, an aberration free optical system does not have a perfectStrehl ratio, a value of unity, due to variations in polarizationresulting from interference of rays at large angles with respect to oneanother. In the present example, the Strehl ratio values are calculatedat field points centered on the point-spread function, i.e., distortioneffects were not considered.

Table 9 shows an aberration free system at 0.75 NA having a Strehl ratioof 0.8434. The performance of the nominal design without intrinsicbirefringence effects is very similar to that of an ideal aberrationfree lens; the Strehl ratio differs over a range of −0.0004 to +0.0005It is understood that the Strehl ratio may exceed that of a perfect lensdue to differences between physical and ideal lens models.

For the compensated system with intrinsic birefringence, the Strehlratio is similar to that of the nominal design without considering theeffects of intrinsic birefringence, and also similar to the ideal 0.75NA aberration free system.

TABLE 9 Strehl Ratio Design Layout On-Axis Field 70% Field Extreme FieldAberration-free 0.8434 0.8434 0.8434 lens (0.75 NA) Nominal, nobirefringence 0.8436 0.8439 0.8430 considered Elements aligned to 0.83890.8377 0.8361 compensate

In summary, this third exemplary embodiment describes a lens with seven[100] optical elements and thirteen [110] optical elements. The relativeclockings of the elements are given in Table 4. When used in a space inwhich the ray angles through the crystal are small with respect theoptical axis, the retardance introduced by the component is small whenthe optical axis is along the [100] crystal axis of the material. Thus,such elements are generally insensitive to clocking, and it is possibleto use the clocking of these components to compensate for manufacturingerrors during fabrication, such as non-rotationally symmetrical defects.For example, the first six [100] optical elements may be varied inclocking without significant loss of performance, according to otherexemplary embodiments. In another exemplary embodiment, the plurality of[100] optical elements may therefore be used to compensate for residualaberrations due to non-rotationally symmetric figure errors on the lenselements more easily than in a lens with more [110] and fewer [100]cubic crystalline elements.

Embodiment 4

The fourth exemplary embodiment for application of the compensationtechniques for intrinsic birefringence may be described in conjunctionwith another exemplary all-refractive projection lens. Such an exemplarylens may be used for photolithography and, in particular, may be used inthe semiconductor manufacturing industry. Such an exemplary lens isprovided in the seventh embodiment disclosed in European Patent No. 1139 138 A1 to Y. Omura. This exemplary lens is depicted in FIG. 1. It isdesigned to operate at a central wavelength of 193.3 nanometers,provides 4× reduction at a numerical aperture of 0.75, and has an imagefield diameter of 27.5 mm. The design employs twenty-eight opticalelements with three aspheric surfaces constructed from calcium fluorideand fused silica; however, each component is assumed to have anintrinsic birefringence of −12×10⁻⁷ in the following calculations usedto illustrate the principles of the present invention. According toother exemplary embodiments, some of the lens elements may be formed ofnon-cubic crystalline material or additional lens elements formed ofnon-cubic crystalline material may be used. Various suitable non-cubiccrystalline materials such as dry fused silica may be used.

RMS and maximum retardance and diattenuation over the exit pupil arelisted in Table 10 for the nominal design without intrinsicbirefringence effects included for relative field heights of 0, 0.7, and1.0. The retardance and diattenuation result from the single-layeranti-reflection coatings used in the model.

TABLE 10 Retardance Relative Field (waves at λ_(o) = 193.3 nm)Diattenuation Height RMS Maximum RMS Maximum 0.0 0.0048 0.0177 0.00680.0273 0.7 0.0052 0.0202 0.0074 0.0296 1.0 0.0055 0.0239 0.0080 0.0358

FIGS. 25A and 25B are graphical representations showing the retardanceacross the system exit pupil due to the anti-reflection coatings for thefield points at the center and edge of the field, respectively. Theretardance is radially-oriented and is largest in magnitude at the edgeof the pupil. FIGS. 26A and 26B are graphical representations showingdiattenuation variation across the pupil for the center and edge of thefield, respectively.

Table 11 shows RMS and peak-to-valley wavefront error for the nominaldesign, without the effects of intrinsic birefringence. Wavefront errorsare given for relative field heights of 0, 0.7, and 1.0 in the Ydirection, and are listed for two orthogonal polarization components.The X component represents the wavefront error for an input polarizationin the X direction assuming a linear polarizer along the X direction atthe system exit pupil. The Y component represents the wavefront errorfor an input polarization in the Y direction assuming a linear polarizeralong the Y direction at the exit pupil. Without cubic crystallineoptical elements, or the effect of intrinsic birefringence considered,the nominal design includes a peak RMS wavefront error of 0.004 waves.

TABLE 11 Peak-to-Valley RMS Wavefront Wavefront Error Error (waves at(waves at Relative λ_(o) = 193.3 nm) λ_(o) = 193.3 nm) Field X Com- YCom- X Com- Y Com- Height ponent ponent ponent ponent 0.0 0.003 0.0030.017 0.017 0.7 0.003 0.004 0.022 0.033 1.0 0.003 0.004 0.022 0.029

FIGS. 27A, 27B, 27C, and 27D show wavefront errors plotted at the systemexit pupil as contour maps for the nominal design without intrinsicbirefringence effects included. FIGS. 27A and 27B show contour plots ofthe residual wavefront error for the exemplary lens depicted in FIG. 1corresponding to an input polarization in the X direction, perpendicularto the field height, used with an exit pupil analyzer in the X directionfor the center and extreme field points, respectively. For the wavefronterror at the central field point, the maximum peak-to-valley opticalpath difference is 0.017 waves at a wavelength of 193.3 nanometers, andfor the wavefront error at the extreme field, the maximum peak-to-valleyoptical path difference is 0.022 waves. FIGS. 27C and 27D show contourplots of the residual wavefront error for the lens depicted in FIG. 1corresponding to an input polarization in the Y direction, parallel tothe field height, used with an exit pupil analyzer in the Y directionfor the central and extreme field points, respectively. For thewavefront error at the central field point, the maximum peak-to-valleyoptical path difference is 0.017 waves at a wavelength of 193.3nanometers, and for the wavefront error at the extreme field, themaximum peak-to-valley optical path difference is 0.029 waves.

Table 12 shows the centroid distortion for the nominal design,calculated based on the point spread function, and the telecentricityerror in the Y direction at relative field heights of 0, 0.7, and 1.0.

TABLE 12 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.00 7.70 0.11 1.0 0.00 10.70 0.51

In an actual lens design using the lens prescription shown schematicallyin FIG. 1 and including cubic crystalline optical elements, intrinsicbirefringence is included. With the effects of intrinsic birefringenceincluded, performance degrades significantly. FIGS. 28A and 28B show thenet retardance across the system exit pupil for field points at thecenter and edge of the field (at object field heights of 0 and 55 mm)according to an exemplary embodiment in which all elements areidentically aligned in three dimensions, with element [110] crystal axesalong optical axis 10. In these plots, the retardance orientationrotates by 90 degrees at one-half-wave intervals, i.e., the effect of a0.75 wave retarder at 0 degrees is the same as a 0.25 wave retarder at90 degrees. Thus, the peak retardance due to intrinsic birefringence inthis example is approximately 2.1 waves at a wavelength of 193.3nanometers.

FIGS. 29A and 29B show the net retardance across the system exit pupilfor field points at the center and edge of the field, respectively,according to another exemplary arrangement in which all elements areidentically aligned in three dimensions, with element [100] crystal axesalong optical axis 10. Again, the retardance orientation rotates by 90degrees at one-half-wave intervals; thus, the peak retardance due tointrinsic birefringence in this example is approximately 1.5 waves at awavelength of 193.3 nanometers.

FIGS. 30A and 30B show the net retardance across the system exit pupilfor field points at the center and edge of the field, respectively,according to another exemplary arrangement in which all elements arealigned identically in three dimensions, with element [111] crystal axesalong optical axis 10. In this exemplary arrangement, the peakretardance due to intrinsic birefringence is approximately 0.8 waves ata wavelength of 193.3 nanometers.

With all elements aligned with their [110], [100], or [111] crystal axesalong optical axis 10, and oriented identically in three dimensions, theretardance produced by intrinsic birefringence produces very largewavefront aberration. Without compensation, this aberration stronglyexceeds the desirable wavefront error required for photolithographyprocesses, particularly for photolithography processes used to producethe small feature sizes in today's semiconductor manufacturing industry.

The fourth exemplary embodiment achieves compensation of the retardanceproduced by intrinsic birefringence by prescribing the orientations ofthe cubic crystal lattice for each element with respect to its opticalaxis, and the relative rotations of those elements about the opticalaxis to correct for intrinsic birefringence of the system. Furthermorein the fourth embodiment, as illustrated in FIG. 31, two of the elementsof the exemplary lens system of FIG. 1 have each been split into twosegments that have the same total thickness and power, with thethicknesses for the two segments and the curvature of the buried surfacebetween them optimized to minimize the net system retardance. Theseadditional degrees of freedom are shown to improve the achievableretardance compensation without requiring redesign of the lens.

According to the fourth embodiment, a combination of [110] opticalelements and [100] optical elements is used to allow the retardancecontributions of the individual elements to substantially cancel eachother and provide an overall wavefront correction that is acceptable forhigh numerical aperture lithography systems.

FIG. 31 is a schematic side view of the improved lens. Lens 100 includesobject plane 80, which may be a reticle or photomask, image plane 82,which may be a substrate upon which the image is formed, optical axis85, and aperture stop, AS, 89. The [100] optical elements, L28A andL28B, are hatched. In this embodiment, all other elements L1-L27B are[110] optical elements aligned with their [110] crystal axes alongoptical axis 85.

The fourth embodiment provides a lens 100 shown in FIG. 31 that includeslens elements L1-L28B having crystal axes and clockings given in Table13. For [110] optical elements, the clocking of each element is givenrelative to an orientation that produces peak birefringence along theoptical axis that is oriented with the retardance axis substantiallyparallel to the X axis (horizontal, in the direction perpendicular tothe specified field of view). For [100] optical elements, the clockingof each element is given relative to an orientation that produces peakbirefringence lobes in the X-Z and Y-Z planes—at radial angles of 0, 90,180, and 270 degrees.

TABLE 13 Crystal Axis Element Clocking Element along Optical Axis(degrees) L1 [110] 51.93 L2 [110] −82.04 L3 [110] −33.00 L4 [110] 71.75L5 [110] −35.37 L6 [110] 27.46 L7 [110] 21.75 L8 [110] −70.79 L9 [110]−43.04 L10 [110] −39.84 L11 [110] 35.04 L12 [110] −63.29 L13 [110] 58.42L14 [110] −3.10 L15 [110] 67.64 L16 [110] 58.53 L17 [110] 49.69 L18[110] 68.53 L19 [110] 29.79 L20 [110] −75.69 L20, Surface 2 ZernikeSurface −75.69 L21 [110] −25.98 L22 [110] 54.09 L23 [110] 42.29 L24[110] 54.60 L25 [110] −21.99 L26 [110] 15.35 L27A [110] −57.40 L27B[110] 68.88 L28A [100] 40.25 L28B [100] 82.87 Image — −0.00000199

The fourth exemplary embodiment illustrates another aspect of thepresent invention, namely, reducing intrinsic birefringence andretardance of a known lens system. This aspect of the present inventionincludes providing a given lens prescription having good opticalqualities and including multiple individual lens elements. For thisgiven lens prescription, at least one of the individual lens elements isreplaced by, or split into, two or more sub-elements. The sub-elementseach include the same overall radius of curvature and include the samethickness so that the overall optical qualities of the lens prescriptionare not adversely affected. For each individual element being replaced,the sub-elements are oriented to reduce net system retardance relativeto the retardance correction achievable using the individual lenselement which they combine to replace.

In one exemplary embodiment, each of the sub-elements may be alignedwith the same crystal axis along the optical axis, and the sub-elementsmay be clocked relative to each other. For example, each of thesub-elements may be a [110] or [100] optical element. In anotherexemplary embodiment, the elements may include different crystal axesaligned along the optical axis, for example, a [100] optical element anda [110] optical element. This concept is illustrated by comparing lens 2in FIG. 1 to lens 100 shown in FIG. 31. Lens 2 shown in FIG. 1 includesmultiple lens elements, including lens elements L101 and L102. Lens 100in FIG. 31 is substantially similar to lens 2 of FIG. 1, with theexception being that lens element L101 of FIG. 1 is replaced by twosub-elements−lens sub-elements L27A and L27B of FIG. 31, and lenselement L102 of lens 2 in FIG. 1 is replaced by two lens sub-elements,namely, lens sub-elements L28A and L28B shown in FIG. 31.

Another effect produced by intrinsic birefringence in the cubic crystallattice is variation of the average index of refraction as a function ofray angle through the crystal. In addition to compensating forretardance errors resulting from intrinsic birefringence, the presentinvention provides for correcting for residual wavefront aberrations anddistortion resulting from the variations in average index of refraction.If uncorrected, this variation in average index of refraction mayproduce astigmatism in the wavefront and may result in distortion of theimage. This distortion may include image shift, image rotation,magnification error, or higher order distortion.

As such, in the fourth embodiment, the optical design includesmodifications, relative to lens 2 of FIG. 1, to compensate for theeffects of variations in average index of refraction. Surface S2 of lenselement L20, the right hand surface of the lens element immediatelyfollowing aperture stop 89, includes a shape defined by Zernikepolynomials as described below. The Zernike coefficients are adjusted tocompensate for residual astigmatism. The Zernike coefficients may beused to adjust the surface shape of other elements and one or multiplesurfaces with an asymmetric variation in curvature, may be utilized inother exemplary embodiments. Also, the radii of curvature of tensurfaces are adjusted to balance residual distortion, and image planerotation is provided to remove residual image rotation. The resultingradii of curvature and Zernike surface coefficients, C_(j) are listed inTable 14, and the image plane rotation is given in Table 13.

The Zernike polynomials, Z_(j), are defined with respect to a circlewith the normalization radius listed. Surface sag, Z(x, y), the integralof which describes the surface, is described by the following equation:${Z\left( {x,y} \right)} = {\frac{c\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {c^{2}\left( {x^{2} + y^{2}} \right)}}} + {\sum\limits_{j = 1}^{4}{C_{j}Z_{j}}}}$where c is the curvature=1/(radius of curvature) and x and y are theCartesian coordinates on the surface.

TABLE 14 Radius of Surface Curvature (mm) L24, Surface S1 277.35519 L24,Surface S2 1289.10376 L25, Surface S1 179.54899 L25, Surface S2446.44705 L26, Surface S1 182.12274 L26, Surface S2 558.39223 L27A,Surface S1 −10831.04108 L27A, Surface S2 154.82711 L27B, Surface S1154.82711 L27B, Surface S2 322.35847 L28A, Surface S1 399.66226 L28A,Surface S2 −2608.81885 L28B, Surface S1 −2608.81885 L28B, Surface S2−1902.32780 Zernike Zernike Parameter Polynomial, Z_(j) Coefficient,C_(j) C₁ x² − y² −1.7603 × 10⁻⁶ C₂ 2xy −2.5077 × 10⁻⁵ C₃ [4(x² + y²) −3](x² − y²)   1.0700 × 10⁻⁵ C₄ 2[4(x² + y²) − 3]xy   1.1000 × 10⁻⁶Normalization — 136.1 mm Radius

In summary, in the fourth embodiment, two elements—lens elements L101and L102 of the exemplary lens prescription shown in FIG. 1, were eachsplit into lens sub-elements L27A and L27B, and L28A and L28B,respectively, to provide improved retardance aberration correction. Ineach case, the radius of curvature of the buried surface producedbetween the two sub-elements and the thicknesses of the two sub-elementswere varied, keeping the total element thickness fixed with respect tothe original lens element. Stated alternatively, the combined thicknessof lens sub-elements L28A and L28B of FIG. 31 is substantially the sameas the thickness of lens element L102 of FIG. 1. Element L101 of FIG. 1is split into two [110] optical sub-components L27A and L27B of FIG. 31to provide fine adjustment of the compensation. The thickness and radiusof curvature of buried surface 83 provide control over the retardanceaberrations at the center and edge of the pupil. Element L102 of FIG. 1is split into two [100] optical sub-components L28A and L28B of FIG. 31to provide fine adjustment of the azimuthal compensation. Each [100]sub-component has the same birefringence as a function of ray angle withrespect to the optical axis; only the azimuthal dependence varies withelement clocking.

Table 15 lists the radii of curvature and thicknesses of the opticalsub-elements produced by splitting components L101 and L102.

TABLE 15 Crystal Axis Direction Element Front Radius Back Radius Ele-for Zero Clocking of Curvature of Curvature Thickness ment Clocking(degrees) (mm) (mm) (mm) L27A [110] −57.40 −10831.04108 154.8271117.96182 L27B [110] 68.88 154.82711 322.35847 32.03818 L28A [100] 40.25399.66226 −2608.81885 17.66426 L28B [100] 82.87 −2608.81885 −1902.3278032.33575

FIGS. 32A and 32B are graphical representations showing the retardanceacross the system exit pupil for the compensated system produced by theintrinsic birefringence and anti-reflection coatings for field points atthe center and edge of the field, respectively. As shown in FIGS. 25Aand 25B, the contribution due the coatings is the same order ofmagnitude as the maximum residual retardance aberrations; thus, thechoice of coating can significant effect the system performance. Adifferent coating design might require re-optimization of the lens toobtain best performance. In the uncompensated system, the contributiondue the coatings is relatively small and the bulk of the retardanceaberration is attributable to intrinsic birefringence.

RMS and maximum retardance over the exit pupil are listed in Table 16for relative field heights of 0, 0.7, and 1.0. These include the effectsof intrinsic birefringence and the single layer anti-reflectioncoatings. The RMS retardance ranges from 0.0029 to 0.0054 waves atλ_(o)=193.3 nm. The compensated system includes a retardance reduced incomparison to the 0.0048 to 0.0055 wave range in RMS retardance due tothe anti-reflection coatings without intrinsic birefringence effects.

TABLE 16 Relative Field Retardance (waves at λ_(o) = 193.3 nm) HeightRMS Maximum 0.0 0.0029 0.0144 0.7 0.0037 0.0266 1.0 0.0054 0.0326

The RMS and peak-to-valley wavefront error are listed in Table 17 forthe compensated design that includes the effects of intrinsicbirefringence. The wavefront errors are given for relative field heightsof 0, 0.7, and 1.0 in the Y direction, and are listed for two orthogonalpolarization components. The X component represents the wavefront errorfor an input polarization in the X direction assuming a linear polarizeralong the X direction at the system exit pupil. The Y componentrepresents the wavefront error for an input polarization in the Ydirection assuming a linear polarizer along the Y direction at the exitpupil. An RMS wavefront error that varies from 0.003 to 0.007 wavesacross the field is achieved. The peak-to-valley wavefront error isreduced by a factor ranging from approximately 47 to 124, compared withexemplary lenses in which all elements are [110], [100], or [111]optical elements oriented substantially identically. Thus, thisembodiment demonstrates that intrinsic birefringence effects can bereduced to a level acceptable for high numerical aperture lithography.

TABLE 17 Peak-to-Valley RMS Wavefront Wavefront Error Error (waves at(waves at Relative λ_(o) = 193.3 nm) λ_(o) = 193.3 nm) Field X Com- YCom- X Com- Y Com- Height ponent ponent ponent ponent 0.0 0.006 0.0030.025 0.017 0.7 0.007 0.006 0.038 0.031 1.0 0.006 0.007 0.045 0.040

In FIGS. 33A, 33B, 33C, and 33D, wavefront errors are plotted at thesystem exit pupil as contour maps. FIGS. 33A and 33B show contour plotsof the residual wavefront error for the lens depicted in FIG. 31corresponding to an input polarization in the X direction, perpendicularto the field height, used with an exit pupil analyzer in the X directionfor the central and extreme field points, respectively. For the centralfield point, the maximum peak-to-valley optical path difference is 0.025waves at a wavelength of 193.3 nanometers, and at the extreme field, themaximum peak-to-valley optical path difference is 0.045 waves. FIGS. 33Cand 33D show contour plots of the residual wavefront error for the lensdepicted in FIG. 31 corresponding to an input polarization in the Ydirection, parallel to the field height, used with an exit pupilanalyzer in the Y direction for the central and extreme field points,respectively. For the central field point, the maximum peak-to-valleyoptical path difference is 0.017 waves at a wavelength of 193.3nanometers, and at the extreme field, the maximum peak-to-valley opticalpath difference is 0.040 waves.

The centroid distortion for the compensated design with intrinsicbirefringence, calculated based on the point spread function, and thetelecentricity error in the Y direction are listed at relative fieldheights of 0, 0.7, and 1.0 in Table 18 below. As shown, the residualdistortion in the X and Y directions is within 0.07 nm, suitable for 157nm lithography. The distortion is also significantly reduced relative tothe distortion of the nominal, uncorrected design given in Table 12.Changes in telecentricity error from the nominal design are negligible.

TABLE 18 Relative Field X PSF Centroid Y PSF Centroid Y TelecentricityHeight Distortion (nm) Distortion (nm) Error (mrad) 0.0 0.00 0.00 0.000.7 0.03 0.01 0.11 1.0 0.00 0.00 0.51

Table 19 provides a summary of Strehl ratio of the design of lens 100 ofFIG. 31. The Strehl ratio values are calculated at field points centeredon the point-spread function, i.e., distortion effects were notconsidered. As shown in Table 19, an aberration free system at 0.75 NAhas a Strehl ratio of 0.8434. The performance of the nominal designwithout intrinsic birefringence effects slightly exceeds the performanceof an ideal 0.75 NA lens by 0.0004 to 0.0017.

For the compensated system with intrinsic birefringence, the Strehlratio is similar to that of the nominal design without considering theeffects of intrinsic birefringence, and relative to a 0.75 NA,aberration-free system.

TABLE 19 On-Axis 70% Extreme Design Layout Field Field FieldAberration-free lens (0.75 NA) 0.8434 0.8434 0.8434 Nominal design, nobirefringence 0.8439 0.8447 0.8451 Elements aligned to compensate 0.84350.8430 0.8428Embodiment 5

The fifth exemplary embodiment for application of the compensationtechniques for intrinsic birefringence may be described in conjunctionwith a catadioptric optical system such as a projection lens forphotolithography that employs a polarization beam splitter. Such anexemplary lens is disclosed as the second embodiment of U.S. Pat. No.6,081,382 by Y. Omura, the contents of which are herein incorporated byreference. This exemplary lens is depicted in the schematic illustrationof FIG. 34. The system advantageously operates at a central wavelengthof λ_(o)=193.3 nm and at a numerical aperture of 0.80. The image fieldis an 8×25 mm rectangular slit field and the lens provides 4× reduction.All lens elements are constructed from fused silica in the exemplaryembodiment, but other materials may be used in other exemplaryembodiments.

For an optical system employing a polarization beam splitter andutilizing polarized input radiation, it is useful to take into accountthe polarization state of the beam through different paths through thesystem. In Embodiment 5, the input polarization may be linear andoriented along the direction of the X-axis; this polarizationcorresponds to s-polarized light upon reflection at polarizationselective surface 208 of beam splitter 240. The X-axis designation isarbitrary and is defined with respect to a Cartesian coordinate systemin which the optical axis of the incoming light beam is designated theZ-direction and the X-axis is parallel to the horizontal direction. Beamsplitter 240 may be coated to maximize the reflectance of s-polarizedlight and the transmittance of p-polarized light.

The exemplary lens system includes object field 230, image field 231,optical axis 248, and aperture stop 233. Beam 249 enters prism 207 ofbeam splitter 240 on the first pass and reflects off polarizationselective surface 208 and travels through prism 207 in a downwarddirection. Upon exiting prism 207 of beam splitter 240, beam 249 travelsthrough quarter wave plate 209 and refractive element 210, reflects fromreflective surface 211 of spherical mirror 212, and returns throughrefractive element 210 and quarter wave plate 209. First quarter waveplate 209 is oriented such that the birefringence axis is at a 45° anglewith respect to the polarization orientation of beam 249 on both passes.The double pass through the wave plate and the reflection fromreflective surface 211 rotates the polarization state of the beam suchthat it is transmitted by polarization selective surface 208 on thesecond pass through beam splitter 240. Following the second pass throughprism 207, beam 249 passes through prism 213 of beam splitter 240 andsecond quarter wave plate 214 having a birefringence axis oriented at45° with respect to the polarization orientation of the beam whichconverts the polarization state to circularly-polarized. This is asdescribed in U.S. Pat. No. 6,081,382.

The root-mean-square (RMS) and maximum retardance over the exit pupilare listed in Table 20 for the nominal design without intrinsicbirefringence effects, for five positions across the 16×100 mm objectfield 230. These result from the single-layer anti-reflection coatingsused in the model and the quarter wave plates; the effects ofpolarization selective surface 208 of beam splitter 240 are alsoincluded in the model assuming perfect reflection for s-polarized lightand perfect transmission for p-polarized light.

TABLE 20 Retardance (waves Object Field at λ_(o) = 193.3 nm) (X, Y) inmm RMS Maximum   (−50, −4) 0.0054 0.0274 (−35, 0) 0.0045 0.0243    (0,0)  0.0044 0.0237   (35, 0) 0.0045 0.0245   (50, 4) 0.0042 0.0233

FIGS. 35A and 35B depict the retardance across the system exit pupil dueto the anti-reflection coatings and wave plates for the field points atthe center and extreme corner of the field (X=50 mm and Y=4 mm at objectfield 230), respectively, for the exemplary lens shown in FIG. 34. FIG.35A shows that, at the center of the field, the retardance is zero atthe center of the pupil and generally increases in magnitude towards theedge of the pupil. At the extreme corner of the rectangular field, theretardance shows a roughly constant linear component, orientedvertically across the exit pupil, as shown in FIG. 35B.

FIGS. 36A, 36B, 36C, and 36D show wavefront errors for the nominaldesign, without the effects of intrinsic birefringence, plotted at thesystem exit pupil as contour maps. FIGS. 36A and 36B show contour plotsof the residual wavefront error for the lens depicted in FIG. 34corresponding to an input polarization in the X direction used with anexit pupil analyzer in the X direction for the center and extreme cornerof the field (X=50 mm and Y=4 mm at the reticle), respectively. For thewavefront error at the central field point shown in FIG. 36A, themaximum peak-to-valley optical path difference is approximately 0.099waves at a wavelength of 193.3 nanometers, and for wavefront error atthe at the extreme field shown in FIG. 36B, the maximum peak-to-valleyoptical path difference is approximately 0.160 waves. FIGS. 36C and 36Dshow contour plots of the residual wavefront error for the lens depictedin FIG. 34 corresponding to an input polarization in the Y directionused with an exit pupil analyzer in the Y direction for the central andextreme field points, respectively. For the wavefront error at thecentral field point shown in FIG. 36C, the maximum peak-to-valleyoptical path difference is approximately 0.093 waves at a wavelength of193.3 nanometers, and for the wavefront error at the extreme field shownin FIG. 36D, the maximum peak-to-valley optical path difference isapproximately 0.152 waves.

The RMS and peak-to-valley wavefront errors are listed in Table 21 belowfor the nominal design, without the effects of intrinsic birefringence,at five exemplary field points. These values represent the wavefronterrors at optimum focus, with tilt terms removed to locate each imagepoint at the center of the wavefront in the calculation. Results aregiven for two orthogonal polarization components. The X componentrepresents the wavefront error assuming a linear polarizer along the Xdirection at the system exit pupil, and the Y component represents thewavefront error assuming a linear polarizer along the Y direction at theexit pupil. The RMS wavefront error is shown to vary over the field from0.011 to 0.016 waves at λ=193 nm.

TABLE 21 Peak-to-Valley RMS Wavefront Wavefront Error Object Error(waves at (waves at Field λ_(o) = 193.3 nm) λ_(o) = 193.3 nm) (X, Y) XCom- Y Com- X Com- Y Com- in mm ponent ponent ponent ponent   (−50, −4)0.015 0.015 0.161 0.149 (−35, 0) 0.016 0.016 0.157 0.162    (0, 0) 0.011 0.011 0.099 0.093   (35, 0) 0.016 0.016 0.161 0.153   (50, 4)0.015 0.015 0.160 0.152

Table 22 shows the centroid distortion for the nominal design,calculated based on the point spread function (PSF), for the same fiveexemplary field points. The maximum image distortion is approximately27.1 nm. The chief ray telecentricity error across the field is within0.4 mrad.

TABLE 22 Object Field X PSF Y PSF (X, Y) Centroid Centroid in mmDistortion (nm) Distortion (nm) (−50, −4) −24.21 −3.38 (−35, 0) −27.13−1.35 (0, 0) 0.00 −0.03 (35, 0) 27.13 1.36 (50, 4) 24.19 3.45

Catadioptric systems with a polarization selective surface generallywork well with a single input polarization state. The polarization statethat is orthogonal to the design input polarization state is lost at thepolarization selective surface. Thus, if the input polarization isfixed, retardance aberrations prior to the polarization selectivesurface couple light out of the system, causing apodization of thetransmitted beam, and contribute a fixed phase to the transmittedwavefront. As such, apodization is advantageously minimized to maintainefficiency and high-performance imaging. This may be achieved when theretardance aberrations prior to the polarization selective surface areeither along or orthogonal to the input polarization state. Thus forthis catadioptric embodiment, retardance aberrations are advantageouslyminimized by properly orienting and shaping lens elements after thesecond wave plate, such as second wave plate 214. For the surfaces priorto polarization selective surface 208, the component of the retardanceaberration that is neither along nor orthogonal to the designpolarization state is advantageously minimized. This approach may bemore helpful than minimizing the retardance in lens elements prior tothe polarization selective surface. Relative designations “before” and“after” are used in reference to the path of a beam traveling from theobject plane to the image plane, throughout the specification.

FIGS. 37A and 37B show the net retardance across the system exit pupilfor field points at the center and extreme corner of the field (X=50 mmand Y=4 mm at the reticle), respectively, in the exemplary embodiment inwhich the components preceding second wave plate 214 are assumed to haveno intrinsic birefringence and in which the components following secondwave plate 214 are [110] optical elements identically aligned in threedimensions, in the exemplary catadioptric optical system illustrated inFIG. 34, at a wavelength of 193.3 nanometers. In the retardance plots ofFIGS. 37A, 37B and similar figures, the retardance orientation rotatesby 90 degrees at one-half-wave intervals, i.e., the effect of a 0.75wave retarder at 0 degrees is the same as a 0.25 wave retarder at 90degrees. Thus, the peak retardance due to intrinsic birefringence forthe exemplary embodiment described in FIGS. 37A and 37B, isapproximately 0.75 waves at a wavelength of 193.3 nanometers, with smallvariation with object field height.

In FIGS. 38A and 38B, the net retardance across the system exit pupil isdepicted for field points at the center and extreme corner of the field,respectively, in the exemplary embodiment in which the componentspreceding second wave plate 214 are assumed to have no intrinsicbirefringence and in which the components following the second waveplate 214 are [100] optical elements identically aligned in threedimensions in the exemplary catadioptric optical system illustrated inFIG. 34, at a wavelength of 193.3 nanometers. The peak retardance due tointrinsic birefringence in this example is approximately 0.60 waves at awavelength of 193.3 nanometers, with small variation with object fieldheight.

FIGS. 39A and 39B show the net retardance across the system exit pupilfor field points at the center and extreme corner of the field,respectively, in the exemplary embodiment in which the componentspreceding second wave plate 214 are assumed to have no intrinsicbirefringence and in which the components following second wave plate214 are [111] optical elements identically aligned in three dimensionsin the exemplary catadioptric optical system illustrated in FIG. 34, ata wavelength of 193.3 nanometers. The peak retardance due to intrinsicbirefringence in this example is approximately 0.90 waves at awavelength of 193.3 nanometers.

Additional performance degradation may result from retardanceaberrations produced by elements preceding second wave plate 214. Inparticular, retardance aberrations produced by elements precedingpolarization selective surface 208 may, in general, cause light tocouple out of the system, resulting in pupil intensity non-uniformity,and this may also change the transmitted wavefront.

With elements following second quarter wave plate 214 identicallyaligned in three dimensions such that their [110], [100], or [111]crystal axes lie along optical axis 248, the intrinsic birefringenceproduces very large retardance aberrations and in turn wavefrontaberrations, as shown in the preceding figures. Without compensation,this unacceptably large aberration significantly exceeds the allowablewavefront error in high-performance photolithography, in particular,photolithography used to produce distortion-free patterns needed intoday's semiconductor manufacturing industry.

For compensating intrinsic birefringence effects in a catadioptricsystem such as described in the present embodiment, there are additionalconsiderations for optimizing the performance compared with compensationin an all-refractive system, such as those described in Embodiments 3and 4.

FIG. 40 is a schematic side view of the lens according to exemplaryembodiment 5, in which each of [110] optical elements 203-206, 218-220,222-224 and 226-227A are hatched. The lens, according to exemplaryembodiment 5, is substantially similar to the lens shown in FIG. 34,with the notable exception being that the refractive lens elements areadvantageously oriented with respect to their crystal lattices andelement 227 of the lens in FIG. 34 is split into two lens elements 227Aand 227B in the lens of the fifth embodiment shown in FIG. 40. Thisexemplary catadioptric system has an NA of approximately 0.80 and mayadvantageously be used to manufacture integrated circuits. Morespecifically, the system may be used in a lithography tool such as astepper, projection printer, or the like, used in the semiconductormanufacturing industry to produce a sequence of patterns on substratesto produce an integrated circuit or other semiconductor device.

Because polarization selective surface 208 is employed in the exemplarycatadioptric system of the fifth exemplary embodiment, it is useful tobalance or minimize the retardance produced by several different groupsof elements. The front group 242 of elements includes the lens elements201-206 preceding beam splitter 240 and the first pass through prism 207of beam splitter 240 up to polarization selective surface 208. Secondgroup 244 comprises the second pass through prism 207 of beam splitter240 following reflection by polarization selective surface 208, firstquarter wave plate 209, refractive lens element 210, and reflectivesurface 211 of spherical mirror 212, and the return path to polarizationselective surface 208 through prism 207. Third group 240 comprises prism213 of beam splitter 240 following transmission through polarizationsensitive surface 208, second quarter wave plate 214, and elements 215and 218-227B between the beam splitter and wafer, also referred to asthe image side of beam splitter 240. Elements 201-206 are disposed onthe object side of beam splitter 240.

According to an exemplary embodiment, input beam 249 is linearlypolarized in the horizontal direction, parallel to the X-axis and in thelong direction of the rectangular object field. For a given ray,depending on the orientation of the local birefringence axis of thecrystal material with respect to the input polarization, the intrinsicbirefringence generally causes the ray to split into two rays withorthogonal polarization orientations. Thus, intrinsic birefringence inthe front group 242 of elements may result in light being lost atpolarization selective surface 208, since light that is polarized in thevertical direction will be transmitted through the beam splitter ratherthan reflected. Since the birefringence magnitude and axis orientationvaries with propagation direction through the crystal, intensitynon-uniformity may result across the system exit pupil.

In the present embodiment, the linear polarization of input beam 249 maybe utilized to minimize the effects of intrinsic birefringence in frontgroup 242. If a given lens element is oriented with its [110] crystalaxis along the common optical axis 248 (see FIG. 5A), and the localbirefringence axis for the ray along the optical axis is orientedhorizontally (i.e., parallel to the input polarization), rays at smallangles with respect to the optical axis correspond to extraordinaryrays, and very little energy will couple into the vertical polarizationstate.

Similarly, if the element is oriented with its [110] crystal axis alongcommon optical axis 248 and the local birefringence axis along theoptical axis is oriented vertically, that is, perpendicular to the inputpolarization, rays at small angles with respect to the optical axiscorrespond to ordinary rays, and very little energy will couple into thehorizontal polarization state.

For a [100] optical element, the birefringence magnitude iscomparatively small for rays at small angles with respect to the opticalaxis. The lens elements may be aligned such that the birefringence lobesare at azimuthal angles of 0, 90, 180, and 270° (see FIG. 5B) in orderto minimize the component of the retardance that is neither parallel nororthogonal to the input polarization state.

In this embodiment, the crystal lattice orientations of the elements infront group 242 are selected from the three crystal lattice orientationsto minimize both the horizontal and vertical variation in retardance.According to other exemplary embodiments of similar catadioptricsystems, and in which circular input polarization is used, and a quarterwave plate is employed immediately prior to the beam splitter to convertthe polarization of the beam to linearly-polarized light, the opticalelements may advantageously be clocked to minimize the RMS retardance,or produce circular residual retardance aberrations to match the inputpolarization state.

Still referring to FIG. 40, the first two lens elements 201 and 202 are[100] optical elements, clocked to have birefringence lobes oriented atazimuthal angles of 0, 90, 180, and 270° in the exemplary embodiment.Lens elements 203, 204, 205, and 206 are oriented so that the opticalaxis is along their [110] lattice directions, with relative clockings of0, 90, 90, and 0°, with respect to an orientation that gives ahorizontal birefringence axis along the optical axis.

Prism 207 of beam splitter 240 is oriented such that its [100] crystalaxis lies along optical axis 248 for the first pass of input beam 249,again with birefringence lobes oriented at azimuthal angles of 0, 90,180, and 270°. Upon reflection from the 45° polarization selectivesurface 208, the beam maintains an equivalent direction through thecrystal. According to another embodiment, beam splitter 240 may be apolarization beam splitter formed of a cubic crystalline material andaligned such that its [110] lattice direction lies substantially alongoptical axis 248 and the local birefringence axis for the ray enteringthe beam splitter along the optical axis is oriented horizontally,parallel to the input polarization orientation, such that uponreflection from the 45° polarization selective surface 208, the beammaintains an equivalent direction through the crystal.

The RMS and maximum retardance over the exit pupil are listed in Table23 for five positions across object field 230; these include the effectsof intrinsic birefringence in the elements 201-206 preceding beamsplitter 240 and segment 207 of beam splitter 240 up to the reflectivesurface 211 of spherical mirror 212, as well as retardance due to thesingle-layer anti-reflection coatings used in the model. The effects ofthe quarter wave plates and polarization selective surface of the beamsplitter are not included.

TABLE 23 X Object Y Object Retardance (waves at Field Field λ_(o) =193.3 nm) Height (mm) Height (mm) RMS Maximum −50 −4 0.0135 0.0799 −35 00.0155 0.0681 0 0 0.0087 0.0350 35 0 0.0138 0.0617 50 4 0.0096 0.0604

FIGS. 41A and 41B depict the retardance across the system exit pupil dueto the intrinsic birefringence of front group 242 and anti-reflectioncoatings for the field points at the center and extreme corner of thefield (X=50 mm and Y=4 mm at the reticle), respectively. FIG. 41A showsthat, at the center of the field, the retardance is zero at the centerof the pupil and increases in magnitude towards the edge of the pupil.At the outer corner of the field, FIG. 41B shows that the retardanceincludes a linear component, oriented roughly horizontally over thepupil.

For the center of the field, the system transmittance varies from anormalized value of 1.0 at the center of the pupil to a minimum value ofapproximately 0.930 at the edge of the pupil. For the extreme or outercorner of the field, the normalized system transmittance varies from 1.0at the center of the pupil, to a minimum of approximately 0.915 at theedge of the pupil. In the second group 244 of elements, in which thebeam reflects off reflective surface 211 and returns to polarizationselective surface 208 of beam splitter 240, there are relatively fewerdegrees of freedom for minimizing the retardance. In this element group,therefore, each individual lens element component may be aligned withits [100] crystal axis along the optical axis, with peak birefringencelobes oriented at azimuthal angles of 0, 90, 180, and 270°. Thisminimizes the component of the retardance that is neither parallel nororthogonal to the axis of the polarization selective surface. Becausethe ray angles are relatively small with respect to the optical axis(within 11° from the optical axis) and the birefringence lobes in thebeam splitter path are preferentially oriented, the effects of theintrinsic birefringence are minimized.

After transmission through polarization selective surface 208 of thebeam splitter, prism 213 of beam splitter 240 is also oriented to be a[100] optical element and oriented to have birefringence lobes at 0, 90,180, and 270°, to minimize the effects of the intrinsic birefringencesince ray angles are small with respect to the optical axis (within 6°)and the birefringence lobes are again preferentially oriented.

According to another embodiment, prism 213 of beam splitter 240 may bealigned such that its [110] lattice direction lies substantially alongoptical axis 248 and the local birefringence axis for the ray travelingalong the optical axis and entering prism 213 is substantiallyperpendicular to the polarization direction of the ray; this embodimentmay be used in conjunction, for example, with a cubic crystalline prism207 oriented such that its [110] lattice direction lies substantiallyalong optical axis 248 and the local birefringence axis for the inputray traveling along the optical axis is substantially parallel to theinput polarization direction, to minimize net retardance.

In the present embodiment, beam splitter 240 may be oriented such thatthe input beam is polarized horizontally, corresponding to s-polarizedlight at the polarization selective surface 208, and polarizationselective surface 208 is coated to preferentially reflect s-polarizedlight. In other exemplary embodiments, the beam splitter may be designedto transmit the beam on the first pass through the beam splitter andreflect the beam on the second pass, and the crystal orientations of thesegments would again be selected to minimize net retardance and maintainan equivalent lattice direction along the optical axis upon reflection.

Third group 246 includes elements 213-227B. For the third group 246 ofelements, compensation of the retardance produced by the intrinsicbirefringence is again achieved by selective orientation of the crystalaxis alignment for each lens element with respect to the optical axis,the relative rotations of those elements about the optical axis, and bysplitting last element 227 of the exemplary lens embodiment shown inFIG. 34, into two sub-elements 227A and 227B that provide the same totalthickness and power but include individual thicknesses and a curvatureof buried surface 250 between them that is optimized to minimizeretardance. As in the previous embodiments, a combination of [110] and[100] optical elements are utilized to allow the retardancecontributions of the individual elements in third group 246 of elementsto be balanced, thereby correcting for intrinsic birefringence andreducing retardance

In this embodiment, elements 215, 221, and 225 and quarter wave plates209 and 214 are [100] optical elements oriented such that the peakbirefringence lobes are oriented at azimuthal angles of 0, 90, 180, and270°. Also, the two sub-elements include the first sub-element 227Aoriented with its [110] crystal axis along optical axis 248 and secondsub-element 227B with its [100] crystal axis along optical axis 248. Thecrystal axis orientation and clockings of each of the components aregiven in Table 24 below. The table includes refractive lens elements201-206, 210, 215, 218-226 and 227A and 227B, beam splitter prisms 207and 213 and wave plates 209 and 214. For [110] optical elements, theclocking of each element is given relative to an orientation thatproduces peak birefringence along the optical axis that is oriented withthe retardance axis substantially parallel to the X axis (horizontal, inthe long direction of the specified field of view). For [100] opticalelements, the clocking of each element is given relative to anorientation that produces peak birefringence lobes in the X-Z and Y-Zplanes, at azimuthal angles of 0, 90, 180, and 270°.

TABLE 24 Crystal Axis Element Direction along Clocking Element OpticalAxis (degrees) 201 [100] 0 202 [100] 0 203 [110] 0 204 [110] 90 205[110] 90 206 [110] 0 Prism 207, [100] 0 Segment 1 Prism 207, [100] 0Segment 2 Wave Plate [100] 0 209, Pass 1 210, Pass 1 [100] 0 210, Pass 2[100] 0 Wave Plate [100] 0 209, Pass 2 Prism 207, [100] 0 Segment 3Prism 213, [100] 0 Segment 4 Wave Plate [100] 0 214 215 [100] 126.80 218[110] 51.77 218, toroidal — −30.00 rear surface S2 219 [110] 149.94 220[110] −81.22 221 [100] 179.17 222 [110] −0.27 223 [110] 60.98 224 [110]45.86 225 [100] −69.14 226 [110] 90.29 227A [110] −30.24 227B [100]11.80

RMS and maximum retardance over the exit pupil are listed in Table 25below for five exemplary field positions and include the effects ofintrinsic birefringence for the elements following the second quarterwave plate 214 and the single layer anti-reflection coatings used in themodel. The RMS retardance ranges from 0.0062 to 0.0084 waves atλ_(o)=193.3 nm, across the field.

TABLE 25 X Object Y Object Field Field Retardance (waves at HeightHeight λ _(o) = 193.3 nm) (mm) (mm) RMS Maximum −50 −4 0.0084 0.0518 −350 0.0078 0.0473 0 0 0.0062 0.0390 35 0 0.0078 0.0473 50 4 0.0084 0.0518

FIGS. 42A and 42B depict the retardance across the system exit pupil forfield points at the center and extreme center and extreme corner of thefield (X=50 mm and Y=4 mm at the reticle), respectively, for thecompensated system as detailed in Table 24, produced by the intrinsicbirefringence of the group of elements following second wave plate 214(in third group 246) and also due to anti-reflection coatings

The total RMS and maximum retardance over the exit pupil are listed inTable 26 for five indicated field positions, including the effects ofintrinsic birefringence for all elements and the single layeranti-reflection coatings used in the model. RMS retardance ranges from0.0076 to 0.0123 waves at λ_(o)=193.3 nm. In one embodiment, RMSretardance may be minimized in the group of elements following thesecond wave plate, rather than the total retardance. Such reduction ofretardance may sufficiently lower levels of retardance for the overallsystem, without the necessity of performing the same optimization on allelement groups.

TABLE 26 X Object Y Object Field Field Retardance (waves at HeightHeight λ _(o) = 193.3 nm) (mm) (mm) RMS Maximum −50 −4 0.0123 0.0824 −350 0.0105 0.0689 0 0 0.0076 0.0493 35 0 0.0113 0.0733 50 4 0.0130 0.0828

FIGS. 43A and 43B are graphical representations depicting the retardanceacross the system exit pupil produced by the intrinsic birefringence ofall elements and anti-reflection coatings for field points at the centerand corner of the field (X=50 mm and Y=4 mm at the reticle),respectively, for the compensated system, as detailed in Table 24.

Similar to the refractive example of Embodiment 3, surface S2 ofrefractive optical element 218 immediately preceding aperture stop 233,is a toroidal surface in which the radius of curvature in orthogonaldirections is varied along with the clocking of the surface tocompensate for astigmatism due to variations in average index ofrefraction. The radii of curvature for the toroidal surface are listedin Table 27 below, and the local X- and Y-axes of the surface arerotated by −30° about the optical axis relative to the system X- andY-axes.

TABLE 27 Radius of Surface Curvature (mm) 218, Surface S2, local Xdirection 1543.4724 218, Surface S2, local Y direction 1543.4659

The fifth exemplary embodiment also illustrates that final element 227of the exemplary lens shown in FIG. 34 and based on a known lensprescription, was split into sub-elements 227A and 227B shown in FIG.40, to provide improved retardance aberration correction. The radius ofcurvature of the buried surface 250 between the elements and thethicknesses of the two segments were varied, keeping the total elementthickness unchanged with respect to single element 227. Table 28provides the radius of curvature and thicknesses of the two segments.

TABLE 28 Crystal Axis Front Direction Element Radius of Back Radius forZero Clocking Curvature of Curvature Thickness Element Clocking(degrees) (mm) (mm) (mm) 227A [110] −30.24 92.4548 263.3382 47.9615 227B[100] 11.80 263.3382 −4239.8801 5.0385

FIGS. 44A, 44B, 44C, and 44D are contour plots of wavefront errorsplotted at the exit pupil for the optical system illustrated in FIG. 40.FIGS. 44A and 44B are contour plots of the residual wavefront errorcorresponding to an input polarization in the X direction used with anexit pupil analyzer in the X direction for the center and extreme cornerof the field (X=50 mm and Y=4 mm at the reticle), respectively. For thewavefront error at the central field point shown in FIG. 44A, themaximum peak-to-valley optical path difference is approximately 0.125waves at a wavelength of 193.3 nanometers, and for wavefront error atthe at the extreme field shown in FIG. 44B, the maximum peak-to-valleyoptical path difference is approximately 0.191 waves. FIGS. 44C and 44Dare contour plots of the residual wavefront error corresponding to aninput polarization in the Y direction used with an exit pupil analyzerin the Y direction for the central and extreme field points,respectively. For the wavefront error at the central field point shownin FIG. 44C, the maximum peak-to-valley optical path difference isapproximately 0.117 waves at a wavelength of 193.3 nanometers, and forthe wavefront error at the extreme field shown in FIG. 44D, the maximumpeak-to-valley optical path difference is approximately 0.192 waves.

The RMS and peak-to-valley wavefront errors are listed in Table 29 forthe compensated design, including the effects of intrinsicbirefringence, at five field points. These values represent thewavefront errors at optimum focus, but tilt terms have been removed tolocate each image point at the center of the point-spread function.Results are given for two orthogonal polarization components. The Xcomponent represents the wavefront error assuming a linear polarizeralong the X direction at the system exit pupil, and the Y componentrepresents the wavefront error assuming a linear polarizer along the Ydirection at the exit pupil.

TABLE 29 Peak-to-Valley RMS Wavefront Wavefront Object Error (waves atError (waves at Field λ _(o) = 193.3 nm) λ_(o) = 193.3 nm) (X, Y) X Y XY in mm Component Component Component Component (−50, −4) 0.018 0.0160.185 0.189 (−35, 0) 0.019 0.017 0.176 0.180 (0, 0) 0.012 0.011 0.1250.117 (35, 0) 0.018 0.017 0.177 0.184 (50, 4) 0.018 0.016 0.191 0.192

Table 29 shows that the RMS wavefront error varies across the field from0.011 to 0.019 waves at λ=193 nm. This is comparable to the range of0.011 to 0.016 waves described in Table 21 for the nominal designembodiment calculated without considering the effects of intrinsicbirefringence The maximum change in RMS wavefront error from the nominaldesign embodiment calculated without considering the effects ofintrinsic birefringence is 0.003 waves. It can be seen that asignificant compensation for wavefront errors caused by intrinsicbirefringence has been achieved by the techniques of the presentinvention. For comparison, according to a comparative exemplaryembodiment in which all elements following the second wave plate are[110] optical elements oriented with the same three-dimensional crystallattice directions, the peak retardance is approximately 0.75 waves, asshown in FIGS. 37A and 37B. The maximum peak-to-valley wavefront errorfor the compensated design with intrinsic birefringence is 0.192 waves,which is comparable to the maximum peak-to-valley wavefront error of0.162 waves for the nominal design without intrinsic birefringence.

Table 30 shows the centroid distortion for the exemplary embodiment inwhich the effects of intrinsic birefringence are compensated for, asdescribed above. This centroid distortion is calculated based on thepoint spread function and is listed for five exemplary field points. Themaximum image distortion is approximately −38.5 nm, and the maximumchange in distortion from the nominal design is approximately −13.8 nm.Distortion was not considered in this embodiment, but further designvariables, such as discussed in conjunction with Embodiments 3 and 4 maybe used to balance changes in distortion due to the intrinsicbirefringence effects in the compensated system. The chief raytelecentricity error across the field is within 0.4 mrad and changes inchief ray telecentricity error are negligible.

TABLE 30 Object X PSF Y PSF Field Centroid Centroid (X, Y) DistortionDistortion in mm (nm) (nm) (−50, −4) −38.01 −5.48 (−35, 0) −38.53 −1.18(0, 0) −0.11 −0.05 (35, 0) 38.26 1.13 (50, 4) 37.70 5.53

Table 31 provides a summary of the performance of the exemplary systemin terms of the Strehl ratio. Strehl ratio values in Table 31 arecalculated at field points centered on the wavefront in the exit pupil(i.e., wavefront distortion effects were removed).

As shown in Table 31, an aberration free system has a Strehl ratio of0.8178 at a numerical aperture of 0.80. For the nominal design withoutintrinsic birefringence effects considered, the Strehl ratio is reducedby a maximum value of 0.0084. For the compensated system with intrinsicbirefringence, the Strehl ratio is reduced from that of an aberrationfree system by a maximum value of 0.0151.

TABLE 31 Object Field (X, Y) in mm Design Layout (−50, −4) (−35, 0) (0,0) (35, 0) (50, 4) Aberration-free lens 0.8178 0.8178 0.8178 0.81780.8178 (0.80 NA) Nominal, no 0.8102 0.8096 0.8134 0.8094 0.8101birefringence considered Elements aligned to 0.8056 0.8063 0.8110 0.80450.8027 compensate

Also as described in conjunction with previous embodiments, one or morestress birefringent elements, wave plates, or combinations thereof mayadditionally be used to correct for residual birefringence variation andconstant residual retardance which remains in the catadioptric systemafter the above-described system corrections have been made.

Referring again to FIG. 40, according to yet another exemplaryembodiment, stress may be applied to a reflective element such as mirrorsurfaces 211 or 216 to alter the base radius of curvature in orthogonaldirections. This stress may correct for residual astigmatism in theexemplary catadioptric optical system. As described in conjunction withembodiment three, the use of at least one optical element whose baseradius of curvature differs in orthogonal directions may additionally oralternatively be used to compensate for residual astigmatism due tovariations in the average index of refraction in the cubic crystallineoptical elements.

According to other exemplary catadioptric embodiments, some of the lenselements may be formed of non-cubic crystalline material or additionallens elements formed of non-cubic crystalline material may be used.Various suitable non-cubic crystalline materials such as dry fusedsilica may be used.

According to still other catadioptric embodiments, the principles of thepresent invention may be applied to catadioptric systems that do notinclude beam splitters or wave plates, such as described in U.S. Pat.No. 6,195,213 B1 to Omura et al., the contents of which are herebyincorporated by reference.

In summary, embodiment five demonstrates that the principles of thepresent invention may be applied to a catadioptric optical system tosignificantly reduce intrinsic birefringence effects and systemretardance, to levels acceptable for high numerical aperturelithography.

Embodiment 6

FIG. 45 shows an exemplary arrangement of an optical system used todemonstrate the basic technique for mitigating the effects of intrinsicbirefringence using an element including a stress-induced birefringence.This illustrated optical system consists of two cubic crystallineoptical elements concentric about focal point 310 of a converging beam.The beam passes through two cubic crystalline elements 302 and 306 whoseradii of curvature are specified to be concentric with focal point 310.Cubic crystalline optical elements 302 and 306 have thicknesses 304 and308, respectively. In an exemplary embodiment, each of thicknesses 304and 308 may be 5 mm and cubic crystalline elements 302 and 306 may beassumed to have a birefringence magnitude, n_(e)−n_(o), of −12×10⁻⁷,corresponding to the intrinsic birefringence of calcium fluoridemeasured at a wavelength of 157 nm. Cubic crystalline optical elements302 and 306 may each be [110] cubic crystalline optical elements alignedalong common optical axis 312, with a relative clocking of 90 degreesabout optical axis 312. According to other exemplary embodiments, therelative clocking of the elements may vary, the crystal orientation ofthe elements may vary, and additional elements may be included.

First optical element 302 includes a compressive hoop stress ofapproximately 19 lbs./in² applied around the perimeter of the element tominimize net RMS retardance of the system. Various techniques may beused to stress the element, and tensile and compressive stresses ofvarious other magnitudes may be used in other exemplary embodiments.

FIG. 46A is a graphical representation depicting the individualretardance contribution due to the stress-induced birefringence of firstelement 302 and excluding the effects of intrinsic birefringence. FIG.46A includes a peak retardance of 0.0142 waves and RMS retardance of0.0047 waves.

FIG. 46B depicts the net retardance for optical system of this exemplaryembodiment including the stress-induced birefringence, and shows amaximum residual retardance of 0.0186 waves and RMS retardance of 0.0065waves. The resulting retardance variation over the pupil shown in FIG.46B is similar to the retardance variation given in FIG. 9C as a resultof the addition of a 2.3 mm thick [100] cubic crystalline third opticalelement. According to the embodiment using the stress-inducedbirefringence, the maximum peak and RMS net retardance values arecomparable to the respective values of 0.0139 and 0.0041 waves for theembodiment described in FIG. 9C. In this manner, stress-inducedbirefringence applied to one of the [110] optical elements is shown toprovide similar correction as the addition of a [100] cubic crystallineelement.

Such application of stress-induced birefringence to a [110] opticalelement of an exemplary optical system including two [110] opticalelements, is intended to be exemplary only. The stress-inducedbirefringence may be applied to the other [110] optical element 306 inanother exemplary embodiment. Furthermore, this technique may beadvantageously applied to various other optical systems includingvarious numbers of elements clocked at various angles with respect toone another. The stress-induced birefringence may be applied to [100],[111] or non-cubic crystalline optical elements such as dry fusedsilica, for example. According to one exemplary embodiment, a third,non-birefringent element may be added to the arrangement shown in FIG.45 (such as the arrangement shown in FIG. 6, for example) and thestress-induced birefringence may be applied thereto.

The previously-described method for measuring or using computer modelingto determine the retardance of an optical system, identifying an opticalelement or elements to have stress-induced birefringence appliedthereto, then applying the compressive or tensile stress as a hoop orother stress to the identified optical element, may be likewise used inthe present embodiment, to produce stress-induced birefringence asdescribed above, and to reduce residual retardance.

The principles described in embodiment 6, may be applied to thepreviously described exemplary lens systems. In particular,stress-induced birefringence may be applied to the illustrated elementsor additional elements added to the illustrated embodiments.

The preceding six exemplary embodiments are intended to be illustrative,not restrictive of the present invention. Furthermore, it is intendedthat the various exemplary techniques for compensating the effects ofintrinsic birefringence, including retardance aberrations, wavefrontaberrations produced by variations in average index of refraction, andvariations in system transmittance, described in conjunction with one ofthe exemplary embodiments, may also be applied to the other exemplaryembodiments. For example, the selection of multiple [110] opticalelements together with at least one [100] optical element, the relativeclocking of the elements, [111] optical elements, stress-inducedbirefringent elements with radially varying stress, stress inducedbirefringent elements with stress varying along axes perpendicular tothe optical axis, the selection of various other lens orientations, theoptimization of lens element thicknesses, spacings, radii of curvatureand aspheric coefficients, and the other exemplary techniques andelements may be used to correct for intrinsic birefringence in thevarious exemplary optical systems. Similarly, another aspect of thepresent invention—the method for compensating for residual astigmatismdue to variations in the average index of refraction in the cubiccrystalline optical elements, through the use of at least one opticalelement whose base radius of curvature differs in orthogonal directions,may be used in any of the previous embodiments.

The preceding merely illustrates the principles of the invention. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the invention and are includedwithin its scope and spirit. Furthermore, all examples and conditionallanguage recited herein are principally intended expressly to be onlyfor pedagogical purposes and to aid in understanding the principles ofthe invention and the concepts contributed by the inventors tofurthering the art, and are to be construed as being without limitationto such specifically recited examples and conditions. Moreover, allstatements herein reciting principles, aspects, and embodiments of theinvention, as well as specific examples thereof, are intended toencompass both structural and the functional equivalents thereof.Additionally, it is intended that such equivalents include bothcurrently known equivalents and equivalents developed in the future,i.e., any elements developed that perform the same function, regardlessof structure. The scope of the present invention, therefore, is notintended to be limited to the exemplary embodiments shown and describedherein. Rather, the scope and spirit of the present invention isembodied by the appended claims.

1. A photolithography tool comprising: a light source outputting lightfor illuminating a reticle; condenser optics positioned to receive lightfrom said light source, said condenser optics positioned to direct anoptical beam formed from said light through said reticle; and projectionoptics configured to form an image of said reticle onto a substrate,said projection optics having an exit pupil, said projection opticsincluding: a first cubic crystalline optical element aligned along anoptical axis, said first cubic crystalline optical element havingintrinsic birefringence that contributes to retardance in said exitpupil, said intrinsic birefringence of said first optical element havingincreased magnitude at a first set of lobes at a first set of locationsarranged in an azimuthal direction about said optical axis; a secondcubic crystalline optical element aligned along said optical axis, saidsecond cubic crystalline optical element having intrinsic birefringencethat contributes to retardance in said exit pupil, said intrinsicbirefringence of said second optical element having increased magnitudeat a second set of lobes at a second set of locations arranged in anazimuthal direction about said optical axis; a third cubic crystallineoptical element aligned along said optical axis, said third cubiccrystalline optical element having intrinsic birefringence thatcontributes to retardance in said exit pupil, said intrinsicbirefringence of said third optical element having increased magnitudeat a third set of lobes at a third set of locations arranged in anazimuthal direction about said optical axis, wherein said first, second,and third cubic crystalline optical elements have a common latticedirection aligned parallel to said optical axis and said first, second,and third cubic crystalline optical elements have their respectivecrystal lattices selectively azimuthally rotated with respect to eachother to reduce retardance over a substantial portion of said exitpupil, said first set of lobes being selectively azimuthally rotatedwith respect to said second set of lobes and said second set of lobesbeing selectively azimuthally rotated with respect to said third set oflobes such that said first set of lobes, said second set of lobes, andsaid third set of lobes are oriented differently with respect to eachother.
 2. The photolithography tool of claim 1, wherein said first,second, and third cubic crystalline optical elements comprise calciumfluoride.
 3. The photolithography tool of claim 1, wherein first,second, and third cubic crystalline optical elements are selectivelyazimuthally rotated such that said second set of lobes is positionedabout said optical axis at locations azimuthally offset from midwaybetween the first set of locations of said first set of lobes and saidthird set of lobes is positioned about said optical axis at locationsazimuthally offset from midway between the second set of locations ofsaid second set of lobes.
 4. The photolithography tool of claim 1,further comprising a fourth cubic crystalline optical element alignedalong said optical axis, said fourth cubic crystalline optical elementhaving intrinsic birefringence that contributes to retardance in saidexit pupil, said intrinsic birefringence of said fourth optical elementhaving increased magnitude at a fourth set of lobes at a fourth set oflocations arranged in an azimuthal direction about said optical axis,wherein said fourth cubic crystalline optical element has a crystallattice selectively azimuthally rotated with respect to the crystallattices of each of the first, second, and third cubic crystallineoptical elements to reduce retardance over a substantial portion of saidexit pupil, said fourth set of lobes being selectively azimuthallyrotated with respect to said third set of lobes such that said fourthset of lobes are oriented differently with respect to said first,second, and third set of lobes.
 5. The photolithography tool of claim 1,wherein said light source comprises a 248 nanometer light sourceoutputting light having a wavelength of 248 nanometers for illuminatingsaid reticle and said projection optics is substantially opticallytransmissive to light having a wavelength of 248 nanometers.
 6. Thephotolithography tool of claim 1, wherein said light source comprises a193 nanometer light source outputting light having a wavelength of 193nanometers for illuminating said reticle and said projection optics issubstantially optically transmissive to light having a wavelength of 193nanometers.
 7. The photolithography tool of claim 1, wherein said lightsource comprises a 157 nanometer light source outputting light having awavelength of 157 nanometers for illuminating said reticle and saidprojection optics is substantially optically transmissive to lighthaving a wavelength of 157 nanometers.
 8. A method of fabricating anoptical system having a pupil comprising: disposing a first cubiccrystalline optical element along an optical axis, said first cubiccrystalline optical element having intrinsic birefringence thatcontributes to retardance in said pupil, said intrinsic birefringence ofsaid first optical element having increased magnitude at a first set oflobes at a first set of locations arranged in an azimuthal directionabout said optical axis; disposing a second cubic crystalline opticalelement along said optical axis, said second cubic crystalline opticalelement having intrinsic birefringence that contributes to retardance insaid pupil, said intrinsic birefringence of said second optical elementhaving increased magnitude at a second set of lobes at a second set oflocations arranged in an azimuthal direction about said optical axis;disposing a third cubic crystalline optical element along said opticalaxis, said third cubic crystalline optical element having intrinsicbirefringence that contributes to retardance in said pupil, saidintrinsic birefringence of said third optical element having increasedmagnitude at a third set of lobes at a third set of locations arrangedin an azimuthal direction about said optical axis; clocking said secondcubic crystalline optical element with respect to said first cubiccrystalline optical element such that said second set of lobes isselectively azimuthally rotated with respect to said first set of lobes;clocking said third cubic crystalline optical element with respect tosaid first cubic crystalline optical element such that said third set oflobes is rotated about the optical axis with respect to said first setof lobes, said third set of lobes and said second set of lobes beingdisplaced by different amounts about said optical axis relative to saidfirst set of lobes, wherein said second and third cubic crystallineoptical elements are clocked so as to reduce retardance over asubstantial portion of said pupil.
 9. The method of claim 8, whereinsaid second and third cubic crystalline optical elements are clocked soas to minimize retardance over a substantial portion of said pupil. 10.The method of claim 8, wherein said second and third cubic crystallineoptical elements are clocked an amount optimized by a computer program.11. A method of fabricating an optical system having an exit pupil, saidmethod comprising: disposing a first cubic crystalline optical elementalong an optical axis, said first cubic crystalline optical elementhaving intrinsic birefringence that contributes to retardance in saidexit pupil; disposing a second cubic crystalline optical element alongan optical axis, said second cubic crystalline optical element havingintrinsic birefringence that contributes to retardance in said exitpupil; and orienting said first and second cubic crystalline opticalelements such that said first and second cubic crystalline opticalelements have respective crystal lattices selectively azimuthallyrotated about the optical axis such that a substantial portion of saidretardance contributed by said first cubic crystalline optical elementis substantially orthogonal to a substantial portion of said retardancecontributed by said second cubic crystalline optical element so as tosubstantially cancel and reduce retardance within the optical system.12. An optical system comprising first and second cubic crystallineoptical elements aligned along a common optical axis, said opticalsystem having an exit pupil, said first and second cubic crystallineoptical elements each having intrinsic birefringence that contributes toretardance in said exit pupil, said intrinsic birefringence of saidfirst cubic crystalline optical element having increased magnitude at afirst set of lobes at a first set of locations arranged in an azimuthaldirection about said optical axis, said intrinsic birefringence of saidsecond cubic crystalline optical element having increased magnitude at asecond set of lobes at a second set of locations arranged in anazimuthal direction about said optical axis, wherein said first andsecond cubic crystalline optical elements have respective crystallattices selectively azimuthally rotated with respect to each other toreduce retardance over a substantial portion of said exit pupil, saidselected azimuthal rotation positioning said second set of lobes aboutsaid optical axis at locations (a) azimuthally offset from the first setof locations of said first set of lobes and (b) azimuthally offset frommidway between the first set of locations of said first set of lobes.13. The optical system of claim 12, wherein at least said first cubiccrystalline optical element comprises a [110] cubic crystalline opticalelement having a [110] crystal lattice direction substantially alignedwith said common optical axis.
 14. The optical system of claim 12,wherein at least said first cubic crystalline optical element comprisesa [100] cubic crystalline optical element having a [100] crystal latticedirection substantially aligned with said common optical axis.
 15. Theoptical system of claim 12, wherein said first and second cubiccrystalline optical elements have a common lattice direction alignedparallel to said common optical axis.
 16. The optical system of claim12, comprising a [111] cubic crystalline optical element having a [b111]crystal lattice direction substantially aligned with said common opticalaxis.
 17. The optical system of claim 12, wherein said first and secondcubic crystalline optical elements have shapes selected to reduceaberration at a wavelength of about 248 nanometers or less.
 18. Theoptical system of claim 12, wherein said first and second cubiccrystalline optical elements have shapes selected to reduce aberrationat a wavelength of about 193 nanometers or less.
 19. The optical systemof claim 12, wherein said first and second cubic crystalline opticalelements have shapes selected to reduce aberration at a wavelength ofabout 157 nanometers.
 20. The optical system of claim 12 having anumerical aperture greater than 0.6.
 21. A cubic crystalline opticalsystem comprising: at least two different cubic crystalline opticalelements each having a different lattice direction aligned along acommon optical axis, said two cubic crystalline optical elements havingtheir respective crystal lattices selectively rotated with respect toeach other and about the optical axis to reduce retardance within theoptical system.
 22. The cubic crystalline optical system of claim 21,wherein at least one of said at least two different cubic crystallineoptical elements comprises a [100] cubic crystalline optical elementhaving a [100] crystal lattice direction substantially aligned with saidcommon optical axis.
 23. The cubic crystalline optical system of claim21, wherein at least one of said at least two different cubiccrystalline optical elements comprises a [110] cubic crystalline opticalelement having a [110] crystal lattice direction substantially alignedwith said common optical axis.
 24. The cubic crystalline optical systemof claim 21, wherein said at least two different cubic crystallineoptical elements comprise a [110] cubic crystalline optical elementhaving a [110] crystal lattice direction substantially aligned with saidcommon optical axis and a [100] cubic crystalline optical element havinga [100] crystal lattice direction substantially aligned with said commonoptical axis.
 25. The cubic crystalline optical system of claim 21,comprising a [111] cubic crystalline optical element having a [111]crystal lattice direction substantially aligned with said common opticalaxis.
 26. The cubic crystalline optical system of claim 21 having anumerical aperture greater than 0.6.
 27. An optical system havingintrinsic birefringence that imparts retardance on light propagatedthrough said optical system, said optical system comprising: a [110]cubic crystalline optical element having a [110] lattice directionaligned along an optical axis, and a [100] cubic crystalline opticalelement having a [100l] lattice direction aligned along said opticalaxis, wherein said two cubic crystalline optical elements have theirrespective crystal lattices selectively rotated with respect to eachother and about the optical axis to reduce said retardance associatedwith said optical system.
 28. The optical system of claim 27 having anumerical aperture greater than 0.6.